The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+19x^12+36x^13+29x^14+26x^15+29x^16+42x^17+30x^18+20x^19+15x^20+5x^22+2x^23+2x^25

The gray image is a linear code over GF(2) with n=32, k=8 and d=12.
This code was found by Heurico 1.16 in 0.00179 seconds.