The generator matrix

 1  0  0  0  1  1  1  0 X^2  1  X  1  1 X^2+X  1  1  X  0  1  1  1  1  1  1  X  X  1  0 X^2  X  1  1  X  1 X^2+X  1  1  1  1  1 X^2+X  1  1 X^2+X  1  1 X^2+X  0  0  1  X  1 X^2+X X^2  0  1  1 X^2+X
 0  1  0  0  0  0 X^2 X^2  1 X+1  1 X+1 X+1  1 X+1  0  X  1  0 X^2+1  X X^2+1  X X^2+1  1  1 X+1 X^2+X  1  X  1 X+1  1  0  1 X^2  X X^2+X X+1  1 X^2+X X^2  1  1  0 X^2  X  1  1 X^2+X  1 X^2+X+1  1  X  1  1 X^2+1 X^2+X
 0  0  1  0  0  1  1  1  0 X+1 X^2+1 X^2  1 X+1  X X^2+X  1  X X+1 X^2+X+1 X+1  X X^2+X X^2 X^2+X  1 X^2+X+1  1 X^2+X  0 X^2+X  1 X+1 X^2+X+1 X+1  0 X^2+X+1 X^2 X^2 X^2+X+1  X X^2+1 X^2  0 X^2+X X+1  1  X X^2+X+1  0  1  X  0  1  1  X X^2+X X^2
 0  0  0  1  1 X^2  1 X^2+1  1 X^2  1  X X+1 X^2+X X^2+1 X^2+X+1 X^2+X+1 X^2+X  1 X^2  0 X+1 X^2+X  0 X^2+X+1 X+1 X^2+X+1 X^2+X X+1  1 X^2+1  1  0 X^2+X+1 X^2+1 X^2+X X+1 X^2+X+1 X^2  X  1 X^2+X+1 X^2+1  0 X^2+X X^2 X^2+X+1  0 X^2+1  0  X  0 X^2+1 X^2+1  0  X X^2+1  1
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 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+720x^52+1152x^54+1728x^56+1484x^58+1292x^60+908x^62+603x^64+228x^66+68x^68+4x^70+4x^72

The gray image is a linear code over GF(2) with n=232, k=13 and d=104.
This code was found by Heurico 1.11 in 614 seconds.