The generator matrix

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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+22x^50+132x^51+326x^52+520x^53+644x^54+690x^55+694x^56+748x^57+787x^58+798x^59+770x^60+582x^61+484x^62+390x^63+219x^64+178x^65+100x^66+30x^67+30x^68+18x^69+8x^70+8x^71+6x^72+2x^73+3x^74+2x^76

The gray image is a linear code over GF(2) with n=232, k=13 and d=100.
This code was found by Heurico 1.16 in 2.98 seconds.