The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X
 0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0
 0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0

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+8x^10+108x^12+8x^14+3x^16

The gray image is a linear code over GF(2) with n=96, k=7 and d=40.
This code was found by Heurico 1.16 in 1.05e-007 seconds.