The generator matrix

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

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+100x^53+296x^54+408x^55+387x^56+472x^57+430x^58+298x^59+351x^60+322x^61+274x^62+220x^63+156x^64+142x^65+114x^66+42x^67+29x^68+34x^69+6x^70+8x^71+4x^72+2x^73

The gray image is a linear code over GF(2) with n=236, k=12 and d=106.
This code was found by Heurico 1.11 in 0.25 seconds.