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  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  X X^2  1  0  X  0  0  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  0 X^2+X  0 X^2  X  0 X^2 X^2+X  X  0 X^2 X^2+X  X  0 X^2+X  X X^2 X^2+X  X  0  0 X^2 X^2+X  X X^2 X^2+X  X X^2+X  X  0 X^2  0 X^2  0 X^2+X  X  0 X^2  0 X^2 X^2+X  0  X  X X^2+X  X  X X^2+X
 0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2
 0  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 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+76x^53+47x^54+16x^55+101x^56+128x^57+110x^58+96x^59+120x^60+104x^61+92x^62+16x^63+29x^64+64x^65+2x^66+12x^69+5x^70+4x^72+1x^104

The gray image is a linear code over GF(2) with n=236, k=10 and d=106.
This code was found by Heurico 1.16 in 45.6 seconds.