The generator matrix

 1  1  1  1  1  1  X  0  1  1  X X^3
 0  X  0 X^2+X X^2 X^3+X^2+X X^2+X  X X^3+X^2  X X^3+X^2+X  X
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^3  0 X^2 X^2 X^3+X^2
 0  0  0 X^3 X^3  0  0 X^3  0  0 X^3 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+182x^10+128x^11+412x^12+128x^13+164x^14+3x^16+6x^18

The gray image is a linear code over GF(2) with n=96, k=10 and d=40.
This code was found by Heurico 1.16 in 0 seconds.