The generator matrix

 1  0  0  1  1  1 X^3+X^2+X X^3  1  1 X^2  1
 0  1  0  1  X X^2+X+1  1  1  X X^3+X+1 X^2  0
 0  0  1  1  1  0  1  X X^2+X+1 X^2+X  1  0
 0  0  0  X X^3 X^3+X X^2+X X^2+X X^2+X X^3+X^2 X^2+X 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+134x^8+632x^9+2312x^10+7312x^11+12000x^12+7296x^13+2320x^14+624x^15+121x^16+8x^17+8x^18

The gray image is a linear code over GF(2) with n=96, k=15 and d=32.
This code was found by Heurico 1.16 in 1.2 seconds.