The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  0  1  X  1  X  1  1  1  1  1  0  1
 0  1  0  0  0  0  0  0  0  1  1  1 X+1  1  X  0 X+1 X+1  X  X  0  X  0
 0  0  1  0  0  0  0  0 X+1  0  1  1  1  X  1  1  X  0 X+1  1  1  X  0
 0  0  0  1  0  0  0  1  1  1  0  X  1  1  X  0  1  0  1  1 X+1  0  0
 0  0  0  0  1  0  1  1  0  1  0  X  1 X+1 X+1  1 X+1 X+1  0 X+1 X+1  0  0
 0  0  0  0  0  1  1  0 X+1  1  X  X X+1  0 X+1  1  1 X+1  X  0 X+1  1  X
 0  0  0  0  0  0  X  0  X  0  0  X  X  X  0  0  X  X  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  0  0  X  0  X  0  X  0  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+51x^14+136x^15+289x^16+472x^17+667x^18+932x^19+1148x^20+1580x^21+1902x^22+1908x^23+1882x^24+1660x^25+1366x^26+972x^27+588x^28+356x^29+223x^30+148x^31+60x^32+28x^33+15x^34

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 11.4 seconds.