The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  1
 0  X  0  X X^3 X^3+X^2 X^2+X X^3+X  X  X  X  0
 0  0  X  X  0  X X^2+X X^3+X^2 X^2+X X^2+X X^3+X^2+X  0
 0  0  0 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2  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+45x^8+228x^9+185x^10+670x^11+1844x^12+668x^13+182x^14+224x^15+44x^16+1x^18+2x^19+2x^20

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.