The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  1  0  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1  0 X+1 X^3  1 X^3+X^2  0
 0  0 X^2  0 X^3+X^2 X^3 X^2  0 X^2 X^3  0  0
 0  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3  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+53x^8+94x^9+217x^10+868x^11+1628x^12+864x^13+238x^14+92x^15+28x^16+2x^17+9x^18+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.