The generator matrix

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

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+28x^57+82x^58+6x^60+4x^62+4x^65+2x^66+1x^72

The gray image is a linear code over GF(2) with n=464, k=7 and d=228.
This code was found by Heurico 1.16 in 0.094 seconds.