The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  1  0  1  1 X^2  1  1  1  0  1  1  X  1  1  X  1  1  0  1  X  1  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  0  0  X  X X^2+X  0  0 X^2+X  X X^2  X X^2+X  X X^2  0 X^2 X^2 X^2+X  0  X X^2+X  X X^2+X X^2+X  X  X X^2  X  0 X^2+X  X  X  X X^2+X  X X^2+X X^2 X^2  0 X^2+X  0  X  X  X X^2+X  0  X X^2+X
 0  0  X  0  X  X  X  0 X^2  0 X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2+X X^2 X^2+X  0 X^2  X  0 X^2+X X^2+X  X X^2  X X^2  0 X^2+X  X  X  0  0 X^2  0 X^2 X^2 X^2+X  X  X X^2  X X^2 X^2+X  0 X^2+X  0 X^2  X  0 X^2+X X^2 X^2+X X^2+X  0  0
 0  0  0  X  X  0  X X^2+X  0  X X^2  X X^2 X^2+X  X  0 X^2  X  X  0 X^2+X X^2 X^2+X X^2+X  0  0 X^2+X  X  X  0  0  0  0  0 X^2  X  X X^2 X^2 X^2+X  X X^2 X^2 X^2 X^2 X^2  0 X^2 X^2+X  X X^2  X  0  X  0  0 X^2 X^2+X X^2+X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 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 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  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+112x^52+212x^54+258x^56+478x^58+458x^60+248x^62+133x^64+72x^66+53x^68+12x^70+8x^72+2x^74+1x^100

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 0.37 seconds.