The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^3
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  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+33x^8+88x^9+66x^10+168x^11+1341x^12+168x^13+60x^14+88x^15+30x^16+2x^18+3x^20

The gray image is a linear code over GF(2) with n=96, k=11 and d=32.
This code was found by Heurico 1.16 in -1.01e-007 seconds.