The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1 X^3+X^2 X^2+X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1 X^3+X X^3+1  1  1
 0  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3
 0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 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+82x^10+320x^11+220x^12+320x^13+76x^14+3x^16+2x^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 6.87e-008 seconds.