The generator matrix

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

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+494x^51+1804x^52+4116x^53+6545x^54+10856x^55+13854x^56+18898x^57+18111x^58+18446x^59+14331x^60+11206x^61+6468x^62+3600x^63+1371x^64+632x^65+189x^66+72x^67+31x^68+26x^69+13x^70+4x^71+2x^73+2x^74

The gray image is a linear code over GF(2) with n=464, k=17 and d=204.
This code was found by Heurico 1.16 in 128 seconds.