The generator matrix

 1  1  1  1
 0  X X^3+X^2 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+16x^3+94x^4+16x^5+1x^8

The gray image is a linear code over GF(2) with n=32, k=7 and d=12.
As d=14 is an upper bound for linear (32,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in -1.01e-007 seconds.