The generator matrix

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

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+90x^55+158x^56+166x^57+155x^58+100x^59+91x^60+56x^61+28x^62+46x^63+44x^64+34x^65+24x^66+12x^67+5x^68+8x^71+5x^72+1x^74

The gray image is a linear code over GF(2) with n=236, k=10 and d=110.
This code was found by Heurico 1.11 in 0.078 seconds.