The generator matrix

 1  1  1  1  1  1  1  1  X  X X^2  1
 0  X  0  X  0 X^2 X^2+X X^3+X X^2 X^2 X^2  0
 0  0  X  X X^3+X^2  X X^2+X  0  X  X X^2 X^3
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3
 0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0

generates a code of length 12 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+46x^8+172x^9+252x^10+960x^11+1192x^12+1032x^13+256x^14+128x^15+41x^16+12x^17+4x^18

The gray image is a linear code over GF(2) with n=96, k=12 and d=32.
This code was found by Heurico 1.16 in 0.031 seconds.