The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1 X^3  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  1  X  1  1 X^2 X^3  1  X  X  1  X  X  1  0  1  1  1 X^3  1  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3 X^2+X  0 X^2+X X^2 X^3+X X^2  X  0 X^2+X X^3+X X^2+X  0  X X^3+X X^2 X^3+X X^3+X^2+X X^3 X^2+X X^2  0 X^2+X  X X^3+X^2+X X^3+X  X X^3+X X^3+X X^3+X^2 X^2 X^2+X X^2 X^3  X  X X^3+X^2 X^3+X X^2+X X^2+X X^3+X  X X^3+X  X X^2+X X^3+X^2+X X^2  X  0 X^3
 0  0 X^3+X^2  0 X^2  0  0 X^3  0 X^2 X^2 X^2 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^3  0 X^3+X^2 X^3  0 X^2 X^3+X^2  0 X^3 X^2 X^3  0 X^2  0 X^2 X^2 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^2  0 X^3 X^3+X^2 X^3 X^3
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^2 X^3 X^3+X^2  0 X^2 X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2  0 X^2 X^3+X^2 X^3  0 X^3 X^2 X^3+X^2  0 X^2 X^2 X^3  0  0 X^3 X^3+X^2  0 X^2  0 X^3 X^2 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  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  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  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+66x^52+130x^53+196x^54+350x^55+472x^56+562x^57+617x^58+556x^59+454x^60+328x^61+161x^62+96x^63+50x^64+10x^65+14x^66+4x^67+10x^68+10x^69+1x^70+2x^71+3x^72+2x^74+1x^90

The gray image is a linear code over GF(2) with n=464, k=12 and d=208.
This code was found by Heurico 1.16 in 0.516 seconds.