The generator matrix

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

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+225x^8+1216x^9+5010x^10+14528x^11+23389x^12+14912x^13+4876x^14+1088x^15+286x^16+2x^18+3x^20

The gray image is a linear code over GF(2) with n=96, k=16 and d=32.
This code was found by Heurico 1.16 in 4.39 seconds.