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.