The generator matrix

 1  1  1  1  1  1  1  1
 0 X^3  0  0  0 X^3 X^3 X^3
 0  0 X^3  0 X^3 X^3 X^3  0
 0  0  0 X^3 X^3  0 X^3 X^3

generates a code of length 8 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+126x^8+1x^16

The gray image is a linear code over GF(2) with n=64, k=7 and d=32.
As d=32 is an upper bound for linear (64,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in 1.05e-007 seconds.