The generator matrix

 1  1  1  1  1  1  X  1  1  X  X  1
 0  X  0 X^2+X X^3+X^2+X X^2 X^3+X^2+X  0 X^3+X^2 X^2+X X^2+X  0
 0  0 X^3+X^2  0 X^2 X^2 X^2 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  0 X^3  0 X^3 X^3  0  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+44x^8+46x^9+162x^10+276x^11+992x^12+272x^13+168x^14+44x^15+35x^16+2x^17+6x^18

The gray image is a linear code over GF(2) with n=96, k=11 and d=32.
This code was found by Heurico 1.16 in 1.05e-007 seconds.