The generator matrix

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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+151x^52+192x^53+471x^54+296x^55+556x^56+320x^57+447x^58+324x^59+391x^60+196x^61+252x^62+128x^63+150x^64+56x^65+98x^66+20x^67+26x^68+4x^69+9x^70+5x^72+3x^74

The gray image is a linear code over GF(2) with n=232, k=12 and d=104.
This code was found by Heurico 1.16 in 0.703 seconds.