The generator matrix

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

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+9x^10+34x^11+173x^12+28x^13+6x^14+2x^15+2x^16+1x^22

The gray image is a linear code over GF(2) with n=96, k=8 and d=40.
This code was found by Heurico 1.16 in 0 seconds.