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

generates a code of length 59 over Z2[X]/(X^3) who�s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+178x^56+80x^58+160x^60+32x^62+38x^64+16x^66+6x^72+1x^96

The gray image is a linear code over GF(2) with n=236, k=9 and d=112.
This code was found by Heurico 1.16 in 13.4 seconds.