The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+114x^55+191x^56+292x^57+234x^58+248x^59+154x^60+224x^61+153x^62+102x^63+74x^64+80x^65+48x^66+52x^67+14x^68+24x^69+21x^70+12x^71+5x^72+4x^73+1x^80

The gray image is a linear code over GF(2) with n=240, k=11 and d=110.
This code was found by Heurico 1.16 in 0.235 seconds.