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

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+121x^64+4x^72+2x^80

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 0.144 seconds.