The generator matrix

 1  1  1  1  X  0  1  1  1  1  X  1
 0  X X^3+X^2 X^2+X X^2+X  X  0  0 X^3+X^2 X^2+X X^2+X  0
 0  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0
 0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0
 0  0  0  0 X^3 X^3  0  0 X^3  0 X^3  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+20x^8+12x^9+157x^10+148x^11+348x^12+148x^13+159x^14+12x^15+15x^16+3x^18+1x^22

The gray image is a linear code over GF(2) with n=96, k=10 and d=32.
This code was found by Heurico 1.16 in 6.87e-008 seconds.