The generator matrix

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

generates a code of length 12 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+60x^9+218x^10+426x^11+666x^12+412x^13+182x^14+60x^15+21x^16+2x^19

The gray image is a linear code over GF(2) with n=96, k=11 and d=36.
This code was found by Heurico 1.16 in 0.015 seconds.