The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^4+1x^8

The gray image is a linear code over GF(2) with n=32, k=6 and d=16.
As d=16 is an upper bound for linear (32,6,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 6.
This code was found by Heurico 1.16 in 6.87e-008 seconds.