The generator matrix

 1  0  1  1  1 X^2+X  1  1  X  1  1 X^2  1  1 X^2  X  1  1  1  1 X^2+X  0  1  1  0 X^2 X^2  X  X X^2 X^2 X^2+X  1  X  X  1  1  1  1  X  1 X^2  1  1  1  0  X X^2  0  1  1  1  X  1  1  1  1  X
 0  1  1 X^2+X X^2+X+1  1 X^2 X+1  1  X X^2+1  1  0  1  1  1 X^2 X^2+1  X X+1  1  1 X^2  1  1  1  1  1  1  1  1  1 X+1  1  1  X X^2+X+1 X^2+X+1 X^2  1 X^2+X+1  1 X^2+1 X^2+X+1 X^2+X  X  1  1  1  0 X^2+X+1  X  1 X^2+X+1 X+1 X+1 X^2  0
 0  0  X  0 X^2+X  0  X X^2  X  X X^2 X^2+X  0  X X^2+X X^2+X X^2+X X^2 X^2+X X^2 X^2  0  0 X^2+X  0  0  X X^2+X  0 X^2  X X^2+X  X X^2+X  0  X X^2+X X^2+X X^2+X  0  X X^2+X  X X^2 X^2 X^2+X X^2  X  X  X  0  0 X^2+X X^2+X X^2+X  X X^2+X  0
 0  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 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+64x^52+116x^53+197x^54+220x^55+198x^56+192x^57+180x^58+184x^59+158x^60+180x^61+129x^62+108x^63+48x^64+24x^65+27x^66+8x^68+8x^70+1x^72+1x^74+1x^76+2x^78+1x^84

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 0.284 seconds.