The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  1  X  0  1  X  1  1
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  1  1  0  X X+1  X  0  0  1  0  1
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  0 X+1  1  1 X+1  X  0  1
 0  0  0  1  1  0  1  1  1  0  1  0  1  0  1  1 X+1  0 X+1 X+1  1 X+1  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  0  X  X  0  0  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  0  0  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  0  X  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  X  0  X  0  X  X  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  X  X  X  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+92x^14+128x^15+276x^16+378x^17+661x^18+914x^19+1279x^20+1672x^21+1765x^22+1992x^23+1801x^24+1676x^25+1306x^26+956x^27+670x^28+360x^29+254x^30+104x^31+65x^32+10x^33+17x^34+2x^35+3x^36+1x^38+1x^40

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 9.64 seconds.