The generator matrix

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

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+73x^16+156x^17+211x^18+256x^19+296x^20+358x^21+425x^22+488x^23+438x^24+406x^25+373x^26+256x^27+162x^28+98x^29+47x^30+24x^31+20x^32+6x^33+2x^36

The gray image is a linear code over GF(2) with n=46, k=12 and d=16.
This code was found by Heurico 1.16 in 0.465 seconds.