The generator matrix

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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+40x^52+86x^53+121x^54+152x^55+180x^56+182x^57+180x^58+212x^59+193x^60+166x^61+161x^62+128x^63+87x^64+74x^65+40x^66+20x^67+6x^68+4x^69+4x^70+4x^72+4x^74+1x^76+1x^78+1x^86

The gray image is a linear code over GF(2) with n=236, k=11 and d=104.
This code was found by Heurico 1.16 in 0.276 seconds.