The generator matrix

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

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+334x^8+2688x^9+9272x^10+31712x^11+42784x^12+32224x^13+9184x^14+2464x^15+369x^16+32x^17+8x^18

The gray image is a linear code over GF(2) with n=96, k=17 and d=32.
This code was found by Heurico 1.16 in 12.7 seconds.