The generator matrix

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

generates a code of length 12 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+60x^10+390x^12+60x^14+1x^24

The gray image is a linear code over GF(2) with n=96, k=9 and d=40.
This code was found by Heurico 1.16 in -6.48e-008 seconds.