The generator matrix
1 0 0 0 0 1 1 1 X 1 1 1 X 1 1 1 1 X X 1 1 0 1
0 1 0 0 0 0 0 0 1 1 X+1 X+1 1 X+1 1 0 X 0 X X+1 0 X X
0 0 1 0 0 0 1 1 1 1 X X+1 X X X+1 X+1 1 1 1 0 0 1 X
0 0 0 1 0 1 1 0 1 0 X+1 1 X+1 X 1 0 X+1 X+1 X+1 X 0 X+1 1
0 0 0 0 1 1 0 1 1 X X+1 X 0 X 1 X 1 X X+1 X+1 X+1 1 X
0 0 0 0 0 X 0 0 0 0 0 0 X X X 0 X X X 0 X 0 0
0 0 0 0 0 0 X 0 0 X X 0 0 X X X 0 X 0 X 0 X X
0 0 0 0 0 0 0 X 0 0 0 X X X X X X X 0 X X X X
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+68x^15+158x^16+224x^17+373x^18+534x^19+583x^20+700x^21+880x^22+980x^23+976x^24+812x^25+682x^26+520x^27+302x^28+180x^29+104x^30+72x^31+25x^32+4x^33+9x^34+2x^35+3x^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 1.16 in 1.7 seconds.