The generator matrix

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

generates a code of length 8 over Z2[X]/(X^4) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+80x^7+93x^8+80x^9+2x^12

The gray image is a linear code over GF(2) with n=64, k=8 and d=28.
As d=29 is an upper bound for linear (64,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 3.81e-009 seconds.