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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+72x^53+169x^54+154x^55+170x^56+232x^57+194x^58+138x^59+180x^60+212x^61+165x^62+142x^63+92x^64+52x^65+34x^66+14x^67+4x^68+4x^69+9x^70+4x^73+4x^74+1x^78+1x^80

The gray image is a linear code over GF(2) with n=236, k=11 and d=106.
This code was found by Heurico 1.16 in 0.298 seconds.