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

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+15x^64+48x^65+111x^66+672x^67+112x^68+48x^69+16x^70+1x^130

The gray image is a linear code over GF(2) with n=536, k=10 and d=256.
This code was found by Heurico 1.16 in 128 seconds.