The generator matrix
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 1 X X X^2 X X 1 X^2 X 1 X X X^3 0 X^2 X^2 X X^2 X X X^3 X^3 0 X^2 X^2 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 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0
generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 59.
Homogenous weight enumerator: w(x)=1x^0+16x^59+8x^60+4x^61+2x^62+1x^64
The gray image is a linear code over GF(2) with n=464, k=5 and d=236.
This code was found by Heurico 1.16 in 0.094 seconds.