The generator matrix

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

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+31x^14+4x^15+102x^16+80x^17+222x^18+208x^19+180x^20+432x^21+437x^22+600x^23+512x^24+432x^25+276x^26+208x^27+200x^28+80x^29+41x^30+4x^31+25x^32+14x^34+4x^36+3x^38

The gray image is a linear code over GF(2) with n=46, k=12 and d=14.
This code was found by Heurico 1.16 in 0.377 seconds.