The generator matrix

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

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+295x^50+1386x^51+3713x^52+7376x^53+12819x^54+20668x^55+28589x^56+35608x^57+39916x^58+36976x^59+29501x^60+20754x^61+12330x^62+6812x^63+3310x^64+1302x^65+541x^66+166x^67+34x^68+14x^69+15x^70+8x^71+4x^72+2x^73+4x^74

The gray image is a linear code over GF(2) with n=464, k=18 and d=200.
This code was found by Heurico 1.16 in 456 seconds.