The generator matrix

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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+124x^64+2x^80+1x^96

The gray image is a linear code over GF(2) with n=256, k=7 and d=128.
As d=128 is an upper bound for linear (256,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.108 seconds.