The generator matrix

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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+154x^51+363x^52+478x^53+607x^54+674x^55+800x^56+768x^57+733x^58+816x^59+671x^60+646x^61+521x^62+330x^63+267x^64+150x^65+80x^66+50x^67+32x^68+20x^69+10x^70+8x^71+10x^72+2x^73+1x^74

The gray image is a linear code over GF(2) with n=232, k=13 and d=102.
This code was found by Heurico 1.16 in 8.08 seconds.