The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1 X^2  1  1  0 X^2 X^2  1 X^2 X^2+X  X  1  1  1  1 X^2  1  1 X^2+X  1  1  0  1  X  0  1 X^2+X X^2 X^2+X  X  X X^2+X X^2  1  1  1  X  1 X^2  1  1  1 X^2  1 X^2  1 X^2+X  1  1
 0  1  0  0  1 X+1  1 X^2+X X^2+1  X  1 X^2+X+1  1  X  1  1  X  X  X X^2 X^2+1  0  0 X^2  1 X+1 X+1  1  X  0  1 X^2+1  1 X^2+X X^2+X  1  1  1  1  1  1  1  1 X^2+X+1  1  1 X^2+1  0 X+1 X^2 X^2+X+1  0 X^2  0 X^2+1  1 X^2+X+1 X^2+X+1
 0  0  1  1  1  0  1  0 X^2 X+1 X+1  X X+1  1  X X^2+1  X  1  1  1 X+1 X+1 X^2+1 X^2  0  0 X+1  0 X^2+X+1 X+1 X+1 X^2+X X^2+X+1  1  X  0 X^2+X X^2+X+1 X^2+X  1 X^2+X X^2+X X^2  X X^2+X+1  X  1  1  0 X^2+1 X^2+X+1  1  X  1 X^2+1  X  0 X^2+X+1
 0  0  0  X X^2+X  0  X X^2 X^2  X  X X^2  X  X X^2 X^2+X  0  0 X^2 X^2  0  0  0 X^2+X X^2+X X^2+X  0 X^2  0 X^2+X X^2  X X^2+X  X  X  X X^2+X  0  0  0 X^2  X  X X^2+X  X X^2  0 X^2+X  0 X^2 X^2+X X^2 X^2 X^2  X  0 X^2  X
 0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 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+166x^51+322x^52+494x^53+618x^54+698x^55+804x^56+766x^57+800x^58+692x^59+668x^60+642x^61+477x^62+410x^63+283x^64+138x^65+80x^66+76x^67+26x^68+8x^69+8x^70+4x^71+8x^72+2x^75+1x^78

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 25.9 seconds.