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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+126x^54+146x^56+306x^58+192x^60+136x^62+35x^64+68x^66+8x^68+2x^70+1x^72+2x^74+1x^104

The gray image is a linear code over GF(2) with n=236, k=10 and d=108.
This code was found by Heurico 1.16 in 10.5 seconds.