The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1 X^3 X^3+X^2+X
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3 X+1 X^3+X^2+X X^2+1  1  1
 0  0 X^2  0 X^3+X^2  0 X^2 X^3 X^2 X^3 X^2 X^3+X^2
 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+246x^10+384x^11+796x^12+384x^13+228x^14+3x^16+6x^18

The gray image is a linear code over GF(2) with n=96, k=11 and d=40.
As d=43 is an upper bound for linear (96,11,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 11.
This code was found by Heurico 1.16 in 0.266 seconds.