10132300201200120300312100000000000
01013230020120012030031210000000000
00101323002012001203003121000000000
00010132300201200120300312100000000
00001013230020120012030031210000000
00000101323002012001203003121000000
00000010132300201200120300312100000
00000001013230020120012030031210000
00000000101323002012001203003121000
00000000010132300201200120300312100
00000000001013230020120012030031210
00000000000101323002012001203003121

That is a [35,12,6] cyclic code over GF(4)

which is the dual to the [35,23,8] cyclic code found by Kschischiang
and Pasupathy.
The latter code has min distance 8, and 15750 words of weight 8.

The weight dist of the former code is;
 wt dist
         1	   2	     3	       4	 5	   6	     7
	 8	   9	    10	      11	12	  13	    14
	15	  16	    17	      18	19	  20	    21
	22	  23	    24	      25	26	  27	    28
	29	  30	    31	      32	33	  34	    35
	 0	   0	     0	       0	 0	   0	     0
	 0	   0	     0	       0	 0	 210	     0
       651	 105	 10080	   17430    110985     76986	506550
    316470   1660680	868560	 3359706   1244250   3785460   1108710
   2383920    471282	698565	   86310     63630	4200	  2475


and the wt dist of its dual, the [35,23,8] code is

 35	     27	 8	    26	9	    25	10	      24  11
r   + 15750 r	s  + 80640 r   s  + 636510 r   s   + 4304160 r	 s

                 23  12		     22	 13		 21  14
     + 26637660 r   s	+ 140419440 r	s   + 661221540 r   s

                   20  15		 19  16		       18  17
     + 2777401200 r   s	  + 10417577940 r   s	+ 34920441360 r	  s

                     17	 18		    16	19		   15  20
     + 104812739850 r	s   + 281178030000 r   s   + 675180827496 r   s

                      14  21		      13  22		      12  23
     + 1446122801760 r	 s   + 2762078950680 r	 s   + 4681275389280 r	 s

                      11  24		      10  25		       9  26
     + 7025380614210 r	 s   + 9268896110880 r	 s   + 10700106003090 r	 s

                       8  27		      7	 28		     6	29
     + 10694957159040 r	 s   + 9171553759740 r	s   + 6638189690160 r  s

                      5	 30		     4	31		   3  32
     + 3984885052932 r	s   + 1927237957680 r  s   + 723056682915 r  s

                     2	33		    34		     35
     + 197101264080 r  s   + 34801303110 r s   + 2981104560 s

so 15750 words of wt 8,

Generator poly for latter code:


x^12+x^10+(w+1)*x^9+(w+1)*x^8+(w+1)*x^7+(w+1)*x^6+(w+1)*x^5+w*x^3+w*x^2+w*x+1

Generator poly for former code:


x^23+x^21+(w+1)*x^20+x^19*w+(w+1)*x^18+x^15*w+x^13+x^12*w+x^9+x^8*w+(w+1)*x^6+(w+1)*x^3+x^2+w*x+1


idempotent corresponding to first poly. is:

(w+1)*x^32+w*x^29+x^28+(w+1)*x^23+(w+1)*x^22+x^21+x^20+(w+1)*x^18+w*x^16+x^14+
w*x^11+x^10+x^9*w+(w+1)*x^8+x^7+x^5+w*x^4+(w+1)*x^2+w*x+1

idempotent corresponding to second poly. is:

(w+1)*x^32+w*x^29+x^28+(w+1)*x^23+(w+1)*x^22+x^21+x^20+(w+1)*x^18+w*x^16+x^14+
w*x^11+x^10+x^9*w+(w+1)*x^8+x^7+x^5+w*x^4+(w+1)*x^2+w*x