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

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+144x^52+32x^53+122x^54+257x^56+224x^57+250x^58+296x^60+224x^61+190x^62+156x^64+32x^65+78x^66+20x^68+17x^72+3x^76+1x^80+1x^92

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 24.6 seconds.