The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0 X+1  1 X+1  0  1 X+1 X+1 X+1  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  0  0  X  X  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  X  X  X  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  0  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+40x^12+164x^14+32x^15+182x^16+192x^17+224x^18+512x^19+592x^20+832x^21+824x^22+960x^23+784x^24+832x^25+688x^26+512x^27+344x^28+192x^29+68x^30+32x^31+89x^32+80x^34+16x^36

The gray image is a linear code over GF(2) with n=46, k=13 and d=12.
This code was found by Heurico 1.16 in 0.888 seconds.