The generator matrix

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

generates a code of length 4 over Z2[X]/(X^4) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+52x^3+149x^4+52x^5+2x^6

The gray image is a linear code over GF(2) with n=32, k=8 and d=12.
As d=13 is an upper bound for linear (32,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in -1.01e-007 seconds.