The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1  0  1  0  1  1  X  1  X  1  1  1  1  0  1 X^2  1  1  1 X^2+X  1  1  1 X^2+X  1  1  1  1 X^2  1  1  1  1 X^2+X X^2+X X^2+X  1  1  1  1  X X^2  0  1  1
 0  1  1  0 X^2+X+1  1 X+1 X^2+X  1 X^2  1 X^2+1  X X+1  1 X^2+X  1  1  0  1 X^2+X  1 X^2+X+1  1 X^2+X+1  0  1 X^2  1  1 X^2+1 X^2  1  0 X+1 X^2  1 X^2 X^2+1  1  X  1  X  1 X^2 X+1  1  1  1 X+1 X^2 X^2  X X^2+X  1  1 X+1  0
 0  0  X  0 X^2+X  0 X^2 X^2  X X^2+X X^2+X X^2 X^2+X  X  X X^2+X  0 X^2  X X^2  0  X  0  X X^2  0 X^2+X X^2 X^2+X  X  X  X X^2  X X^2 X^2+X X^2  0  0 X^2+X  X  0  0  0  0  X  0 X^2+X  0  0  X  X X^2+X X^2 X^2 X^2+X X^2 X^2+X
 0  0  0  X  0  0  0 X^2 X^2 X^2  0  0 X^2  X  X X^2+X  X X^2+X  X X^2+X  X  X X^2+X X^2+X X^2  0  X X^2+X X^2  0 X^2+X X^2+X X^2 X^2+X X^2+X X^2  X  0 X^2+X X^2 X^2  X  0 X^2 X^2  X  0  0  0  X X^2+X  0  0  X  0 X^2+X  0  X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  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+70x^51+162x^52+176x^53+414x^54+256x^55+512x^56+286x^57+467x^58+312x^59+459x^60+198x^61+362x^62+166x^63+126x^64+30x^65+26x^66+16x^67+15x^68+10x^69+6x^70+10x^71+5x^72+4x^73+3x^74+2x^75+2x^78

The gray image is a linear code over GF(2) with n=232, k=12 and d=102.
This code was found by Heurico 1.16 in 0.833 seconds.