The generator matrix

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

generates a code of length 12 over Z2[X]/(X^4) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+92x^11+68x^12+92x^13+1x^14+1x^16+1x^18

The gray image is a linear code over GF(2) with n=96, k=8 and d=44.
As d=46 is an upper bound for linear (96,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 0 seconds.