The generator matrix

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

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+122x^55+153x^56+276x^57+267x^58+278x^59+200x^60+174x^61+130x^62+150x^63+64x^64+64x^65+34x^66+46x^67+14x^68+18x^69+18x^70+12x^71+8x^72+12x^73+7x^74

The gray image is a linear code over GF(2) with n=240, k=11 and d=110.
This code was found by Heurico 1.11 in 0.141 seconds.