The generator matrix

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

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+25x^12+40x^13+31x^14+30x^15+23x^16+28x^17+22x^18+16x^19+13x^20+12x^21+11x^22+2x^23+2x^24

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 0.00188 seconds.