The generator matrix

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

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+88x^14+104x^15+272x^16+444x^17+678x^18+884x^19+1298x^20+1632x^21+1720x^22+2000x^23+1788x^24+1688x^25+1364x^26+1000x^27+652x^28+320x^29+224x^30+104x^31+83x^32+12x^33+22x^34+4x^35+2x^36

The gray image is a linear code over GF(2) with n=46, k=14 and d=14.
This code was found by Heurico 1.16 in 10.5 seconds.