The generator matrix

 1  0  0  0  0  0  0  0  1  1  1  1  1  0  X  X  0  X  1  1  0  1  1
 0  1  0  0  0  0  0  0  0  0  1  1  1  X  1  X  1  0  1 X+1  0  0  0
 0  0  1  0  0  0  0  0  0  1  0 X+1  1  X  0  1  X  1  1  1  0  0  0
 0  0  0  1  0  0  0  0  1  0  0 X+1  1  1  1 X+1 X+1  0  X  1  1  0  0
 0  0  0  0  1  0  0  0  1  1  X  0 X+1 X+1  0  1  X  0  1  1  X  0  0
 0  0  0  0  0  1  0  0  1  X X+1  X  1  X X+1 X+1  1  1 X+1 X+1  X  X  0
 0  0  0  0  0  0  1  0  1 X+1  X X+1  X X+1  X X+1 X+1  1  X X+1  1  0  0
 0  0  0  0  0  0  0  1  X  1 X+1 X+1  0 X+1  1  1  0 X+1  X  0  0  0  0

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+103x^12+662x^14+2170x^16+5248x^18+10096x^20+14550x^22+14372x^24+10032x^26+5507x^28+2034x^30+633x^32+112x^34+14x^36+2x^38

The gray image is a linear code over GF(2) with n=46, k=16 and d=12.
This code was found by Heurico 1.11 in 26.8 seconds.