The generator matrix

 1  0  0  1  1  1 X^3+X X^3+X  1 X^3+X X^3+X^2+X  1  1  1  1  1  1  1  0  X  X  0  1  1  X  1  1  1  1  1  X  1 X^3+X^2  X  0  X  1  1  1  1 X^3+X^2+X X^2  X X^3+X^2 X^3+X  1 X^3  0  1  1 X^2 X^3 X^2  1  1  1  1  1
 0  1  0  0 X^2+1 X+1  1  1 X^2+X X^2  1 X^2+1 X^3+X+1 X^2+X X^3+X^2 X^3+1 X^3+X X^3+X^2+X+1  1  1  0  1 X^2  1  1  1 X^2+X X^3+X^2+X X^3+X X^2+X+1 X^3+X^2+X X^3  1  1  X  1 X^2  1 X^3+X^2+1 X^3+X+1  1 X^3+X^2  1  1 X^3+X^2 X^3+1  X  1 X^3 X^3+X  1  1  1 X^2 X^3 X^3+X+1 X^3  0
 0  0  1  1  1  0  1  X X^3  1 X^2+X+1 X^3+X^2+X+1 X^3+X^2+X X^3+1 X^3+X^2+X X^2+X X^3+X^2+X+1 X^2+1 X+1  X  1 X^3+X X^3+X+1 X^3+X^2+X+1 X^3+1 X^3 X^2+X X^2+1 X^3+X^2 X^3+X+1  1 X^3+X  0 X^3+X+1  1 X+1 X^3+X^2+X+1 X^2+X+1 X^3+X^2 X^2+X+1 X^3+X^2  1  0 X^3+X+1  1 X^3+X  1  0 X^3+X+1  X X^3+X^2+1 X^2+X  X X^3+X^2 X+1  0 X^2 X^2+X
 0  0  0  X X^3+X X^3 X^3+X X^2  0  X X^2+X X^3+X^2+X X^3 X^3+X^2+X X^2  0  X X^2+X X^3+X X^3+X^2+X X^3+X^2  X X^3+X^2+X X^3  0 X^3+X^2+X X^2+X X^2 X^2+X X^3+X^2  X X^2+X X^3+X^2 X^3+X^2  0  0 X^3+X X^2 X^2 X^3+X  X X^3+X^2 X^3  0 X^2+X X^3+X X^3+X^2+X X^3+X X^3+X^2 X^3+X^2+X X^3 X^2 X^2+X  0  X X^2+X X^3+X^2  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+254x^52+1050x^53+1943x^54+2844x^55+3798x^56+4318x^57+4606x^58+4428x^59+3813x^60+2738x^61+1400x^62+836x^63+440x^64+138x^65+114x^66+20x^67+9x^68+12x^69+1x^70+5x^72

The gray image is a linear code over GF(2) with n=464, k=15 and d=208.
This code was found by Heurico 1.16 in 12 seconds.