The generator matrix

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

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+62x^52+98x^54+265x^56+256x^57+714x^58+256x^59+257x^60+70x^62+37x^64+14x^66+16x^68+1x^72+1x^108

The gray image is a linear code over GF(2) with n=464, k=11 and d=208.
This code was found by Heurico 1.16 in 0.25 seconds.