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.