The generator matrix

 1  0  0  1  1  1  0  1 X^2  1  1  X X^2+X  1  1  X  0  1  1  1 X^2 X^2+X  1  1  0 X^2 X^2+X  1  1 X^2 X^2  1  1  0  1  X  1 X^2+X X^2+X  X  1  1  1  1  1  0  1  1  1  1 X^2+X  1  1 X^2  1  1  1  1  1  X
 0  1  0  0  1 X^2+1  1  X  1  1 X^2+X  1 X^2 X^2+X+1  0  1 X^2+X X^2+X+1 X^2  1  1  1 X^2+X X^2+X+1  1 X^2+X  1  X X+1  1  1  1 X^2  1 X^2+X+1  1 X^2+1  1  1  1  1 X^2+1 X^2  X X^2+1 X^2  X  1 X+1  1  1  1 X^2+X+1  1 X^2+X X^2+X X^2+1  0 X^2+X+1  0
 0  0  1 X+1 X^2+X+1  0 X+1 X^2+1 X^2+X  1 X^2 X^2+1  1 X^2  1 X^2+X  1  1 X^2+X  X  1 X^2 X^2+X+1 X^2+X X^2+X+1  1  X  0 X^2+1 X^2+X+1  1 X^2+1  1  X X+1 X^2+X+1 X^2  0 X^2+X  1  0 X^2+X  X X+1  1  1  X  0 X^2+X  X X+1 X+1  1  0  X X^2+X+1 X^2+1  X  1  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  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+130x^55+208x^56+280x^57+231x^58+180x^59+220x^60+184x^61+139x^62+118x^63+106x^64+56x^65+67x^66+50x^67+30x^68+24x^69+10x^70+7x^72+2x^75+4x^76+1x^78

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 0.247 seconds.