The generator matrix

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

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+148x^10+208x^11+360x^12+160x^13+108x^14+16x^15+23x^16

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.