The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  1  X  1  0  1  1  1  1  X  1  1
 0  1  0  0  0  0  0  X X+1  X  1 X+1  0  0  1  0  X X+1  1  0  0  1  0
 0  0  1  0  0  0  0  0  1 X+1  X X+1  X  1 X+1  1  1  0  1  0  X X+1  0
 0  0  0  1  0  0  0  0  0  0  0  0  0 X+1  1  X  X  1  X X+1  1  X  1
 0  0  0  0  1  0  0  1  0 X+1  X  0  1  1  1  1  0  X  0  X  0  1  1
 0  0  0  0  0  1  0  1  X  X  1 X+1  X  X  0 X+1  0  0  1  1 X+1  0  0
 0  0  0  0  0  0  1  1 X+1  0  1  X  0  X  1 X+1 X+1  X  1 X+1  X X+1  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+37x^14+148x^15+338x^16+408x^17+633x^18+908x^19+1279x^20+1666x^21+1791x^22+1876x^23+1791x^24+1710x^25+1375x^26+1000x^27+613x^28+350x^29+248x^30+96x^31+74x^32+26x^33+12x^34+4x^35

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 12.7 seconds.