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 X 1 1 X 1 1 X 1 1 X X 1 X X 1 X^2 X X X 1 X^2 X X 1 X X^2 X^3 X^2 0 X X^2 X X^2 X^2 X^3 X X^3 0 X^2 X^3 1
0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 0 0 0
generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+1x^64+28x^65+2x^66
The gray image is a linear code over GF(2) with n=504, k=5 and d=256.
This code was found by Heurico 1.16 in 0.14 seconds.