The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+103x^56+172x^57+136x^58+172x^59+108x^60+44x^61+60x^62+36x^63+47x^64+48x^65+30x^66+32x^67+12x^68+8x^69+12x^70+1x^72+2x^74

The gray image is a linear code over GF(2) with n=240, k=10 and d=112.
This code was found by Heurico 1.11 in 0.078 seconds.