The generator matrix

 1  0  0  1  1  1 X^3+X^2+X  1  1  1  1  1
 0  1  0  1 X^2+X X^2+X+1  1 X^3+X^2 X^3+X^2 X^3+X X^3 X^3
 0  0  1  1 X+1  X X+1  X X^2+X+1 X^2+X+1  0 X^3
 0  0  0 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3+X^2 X^2 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+94x^8+286x^9+1152x^10+3422x^11+6476x^12+3440x^13+1132x^14+272x^15+101x^16+2x^17+4x^18+2x^19

The gray image is a linear code over GF(2) with n=96, k=14 and d=32.
This code was found by Heurico 1.16 in 0.312 seconds.