The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 1 1 X 1 1 X 0 0 1 1
0 1 0 0 0 0 0 0 0 0 0 1 X 1 1 1 1 X+1 X 1 X X+1 0
0 0 1 0 0 0 0 1 1 1 0 1 1 X X+1 X+1 1 X+1 1 X+1 0 1 X+1
0 0 0 1 0 0 0 1 X X+1 1 X+1 1 X X X+1 X 0 X 1 X X+1 1
0 0 0 0 1 0 1 0 1 X+1 X+1 0 X+1 X X+1 X X+1 X X 1 1 X+1 0
0 0 0 0 0 1 1 X+1 0 1 X X 0 0 X+1 X+1 X X 1 0 X+1 1 X
0 0 0 0 0 0 X X 0 0 0 0 X X 0 X X 0 0 X X X 0

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+74x^15+154x^16+224x^17+366x^18+498x^19+609x^20+756x^21+888x^22+924x^23+940x^24+868x^25+684x^26+492x^27+310x^28+188x^29+104x^30+58x^31+33x^32+12x^33+6x^34+2x^35+1x^36

The gray image is a linear code over GF(2) with n=46, k=13 and d=15.
This code was found by Heurico 1.10 in 0.61 seconds.