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  X  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  X  1  1  X  1 X^2  1  1  X  1  1  1  1  X  X  1  1  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0 X^2 X^3 X^3 X^2  0 X^3+X^2  0 X^3+X^2 X^3+X^2  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2  0
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2  0 X^2  0 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2  0 X^2 X^3 X^2  0  0 X^3+X^2  0 X^2 X^2 X^3  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3  0 X^2  0  0 X^3+X^2 X^3 X^3 X^3  0  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^2  0 X^3+X^2 X^3  0 X^2 X^2 X^3 X^3  0 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0  0  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  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+32x^52+54x^53+61x^54+80x^55+119x^56+404x^57+654x^58+370x^59+74x^60+60x^61+34x^62+28x^63+17x^64+22x^65+13x^66+2x^67+10x^68+2x^69+5x^70+3x^72+2x^73+1x^98

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 0.266 seconds.