The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  0  X  X  X  0  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  0  X  0  X  X  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  0  X  0  X  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  0  X  X  X  X  0  X  X
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  X  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  X  0  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  0  0  0  X  X  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+30x^14+102x^16+128x^18+64x^19+84x^20+256x^21+118x^22+384x^23+192x^24+256x^25+176x^26+64x^27+104x^28+42x^30+25x^32+16x^34+4x^36+2x^38

The gray image is a linear code over GF(2) with n=46, k=11 and d=14.
This code was found by Heurico 1.16 in 0.116 seconds.