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.