The generator matrix

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

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+31x^8+192x^9+160x^10+1088x^11+1152x^12+1088x^13+160x^14+192x^15+31x^16+1x^24

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.