The generator matrix

1 0 0 0 0 0 0 1 1 1 0 1 1 0 X 0 1 X 1 X X X 1
0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 X X 1 X 1 1 X 1
0 0 1 0 0 0 0 0 1 1 X 0 X+1 1 X 1 0 X+1 0 X+1 0 X 0
0 0 0 1 0 0 0 1 0 X 1 X+1 X X 1 X X+1 X X X X+1 1 0
0 0 0 0 1 0 0 1 X X+1 X X+1 X 1 X+1 X+1 1 0 1 X X 1 0
0 0 0 0 0 1 0 1 X+1 0 1 X 0 X X+1 X+1 1 X X+1 X+1 X 1 0
0 0 0 0 0 0 1 X 1 X 1 X+1 0 0 X 1 1 X+1 X X+1 X 0 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+73x^14+130x^15+295x^16+432x^17+664x^18+954x^19+1211x^20+1544x^21+1787x^22+2006x^23+1853x^24+1644x^25+1337x^26+962x^27+673x^28+400x^29+224x^30+104x^31+63x^32+12x^33+11x^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 1.10 in 2.08 seconds.