The generator matrix

 1  0  0  0  1  1  1  0  0 X^2  1  1  1  1 X^2+X X^2  1 X^2+X X^2  1  1 X^2  1  1  1  X  1  1  1  1  1 X^2+X X^2+X  0  1  1 X^2  X X^2+X  X X^2  1  0  1  X  X  1  1  1  X X^2  1 X^2+X X^2+X X^2 X^2  1 X^2  1
 0  1  0  0  0 X^2 X^2 X^2  1  1 X+1  1  1 X^2+1  1  1  X X^2+X  0 X^2+X X+1  X X^2 X+1 X^2+X  1 X+1  1  0  X  0  1  1 X^2+X  1  X  1  1  X  1 X^2 X^2+X+1  1  0 X^2  1  1 X^2+1 X^2+X X^2 X^2+X  X  1 X^2  1 X^2 X^2+X+1  1 X^2
 0  0  1  0 X^2  1 X^2+1  1 X+1  0  1 X^2+X X^2 X+1 X+1  X  0  1  1 X+1 X^2+X X^2  X  0  1 X^2+X+1 X^2+X+1  1 X+1  X  X  X X^2+X  1 X+1 X^2+1  1  1  1  0  1 X+1 X^2+X X^2+X+1  X X^2+X  X X^2+1 X^2+X+1  1 X^2+X X^2+X+1 X+1  1  1 X^2+X X+1 X^2+1 X^2
 0  0  0  1 X^2+X+1 X^2+X+1  0 X+1 X^2  1  1  1 X^2  0 X^2+X+1 X^2 X^2  1  X X^2+X X+1  1  1  X X^2+1  X  0 X+1 X+1 X+1 X^2+X  X X^2+1 X^2+X  X  X X+1 X^2+X+1 X+1 X^2+1 X^2+1  1 X+1 X^2+1  1 X^2 X^2+X  1  X X+1  1 X+1 X^2 X^2  0  1 X^2+X+1  X 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+106x^53+268x^54+422x^55+408x^56+442x^57+439x^58+342x^59+336x^60+280x^61+305x^62+210x^63+171x^64+132x^65+81x^66+74x^67+24x^68+30x^69+11x^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 1.16 in 0.587 seconds.