The generator matrix

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

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+141x^52+40x^53+242x^54+104x^55+257x^56+112x^57+262x^58+112x^59+320x^60+104x^61+174x^62+40x^63+89x^64+26x^66+15x^68+3x^72+4x^76+2x^80

The gray image is a linear code over GF(2) with n=232, k=11 and d=104.
This code was found by Heurico 1.16 in 0.271 seconds.