The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  0  1  1  1  1  1  X  X
 0  1  0  1  0  1  1  0  0  1  1  1  1  0  X  1  0 X+1  1  1  1  1  1
 0  0  1  1  1  0  1  0  1  1  0  0  1  1  1  X  0  0  1  1  1 X+1  1
 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  X  0  0  X  X  0  X  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  0  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  0  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  0  0  X  X  X  X
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  X  0  0  X
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  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+88x^12+16x^13+133x^14+176x^15+617x^16+720x^17+1088x^18+1856x^19+2588x^20+3360x^21+3765x^22+4128x^23+3491x^24+3360x^25+2600x^26+1856x^27+1288x^28+720x^29+511x^30+176x^31+114x^32+16x^33+88x^34+4x^36+7x^38+1x^40

The gray image is a linear code over GF(2) with n=46, k=15 and d=12.
This code was found by Heurico 1.16 in 10.2 seconds.