The generator matrix
1 0 0 0 1 1 1 1 0 1 1 X 1 X X 0 1 1 1 1 1 1 1
0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 X 0 X 0 0 0
0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 X+1 1 1 0 0 0
0 0 0 1 1 1 0 0 1 1 0 1 X+1 X X+1 1 1 1 1 0 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X 0 0 X X 0 0 0
0 0 0 0 0 X 0 0 0 0 0 X X 0 0 X 0 X X 0 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X X 0 X 0 0 0 0 X X 0
0 0 0 0 0 0 0 X 0 0 0 X X X X X 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 X X X 0 0 X X X 0
0 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 X X 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 0 0 X X X X 0
generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+142x^12+228x^14+196x^15+950x^16+616x^17+1388x^18+1876x^19+2570x^20+3136x^21+2896x^22+5096x^23+2928x^24+2128x^25+2584x^26+2856x^27+1378x^28+256x^29+964x^30+212x^31+217x^32+8x^33+124x^34+4x^35+6x^36+8x^38
The gray image is a linear code over GF(2) with n=46, k=15 and d=12.
This code was found by Heurico 1.16 in 10.6 seconds.