The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  1  1  1  1  0  1  0  X  0  1  X  1
 0  1  0  0  0  0  0  0  0  0  X  1  1  1 X+1  1  0  1  1  1 X+1  1  1
 0  0  1  0  0  0  0  0  0  0 X+1  X X+1  1 X+1 X+1  1  0 X+1  1  X X+1  0
 0  0  0  1  0  0  0  1  1  1  1 X+1  X  X X+1  0  1  0 X+1  1  1  0  1
 0  0  0  0  1  0  1  1  0  1  0  0  X X+1  1  X  1  1  0  0  X X+1 X+1
 0  0  0  0  0  1  1  0  1  1  0  X  X  1  0  1  1  1  0  X X+1  0 X+1
 0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  X  X  0  0  0  X  X  X
 0  0  0  0  0  0  0  0  X  X  0  0  X  0  X  0  X  X  X  0  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+242x^14+1064x^16+2577x^18+4910x^20+7588x^22+7572x^24+4938x^26+2601x^28+1026x^30+235x^32+13x^34+1x^44

The gray image is a linear code over GF(2) with n=46, k=15 and d=14.
This code was found by Heurico 1.16 in 48 seconds.