The generator matrix

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

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+746x^52+2122x^53+3751x^54+5622x^55+7677x^56+8140x^57+9647x^58+8454x^59+7574x^60+5312x^61+3506x^62+1782x^63+730x^64+260x^65+135x^66+42x^67+22x^68+6x^69+1x^70+4x^71+2x^72

The gray image is a linear code over GF(2) with n=464, k=16 and d=208.
This code was found by Heurico 1.16 in 43.1 seconds.