The generator matrix

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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+497x^52+1938x^53+4068x^54+6772x^55+10959x^56+13930x^57+17745x^58+18762x^59+18214x^60+15004x^61+10632x^62+6334x^63+3548x^64+1506x^65+737x^66+238x^67+147x^68+22x^69+2x^70+6x^71+6x^72+4x^76

The gray image is a linear code over GF(2) with n=472, k=17 and d=208.
This code was found by Heurico 1.16 in 128 seconds.