The generator matrix

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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+156x^55+80x^56+184x^57+88x^58+188x^59+22x^60+96x^61+32x^62+84x^63+21x^64+40x^65+12x^67+2x^68+2x^72+8x^74+8x^75

The gray image is a linear code over GF(2) with n=236, k=10 and d=110.
This code was found by Heurico 1.16 in 36 seconds.