The generator matrix

 1  1  1  1  X  1  1  X  X  X  1  1
 0 X^3+X^2 X^3 X^2 X^3+X^2  0 X^3 X^2  0 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 12.

Homogenous weight enumerator: w(x)=1x^0+60x^12+3x^16

The gray image is a linear code over GF(2) with n=96, k=6 and d=48.
As d=48 is an upper bound for linear (96,6,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 6.
This code was found by Heurico 1.16 in 3.81e-009 seconds.