The generator matrix

 1  0  0  1  1  1  0 X^2  1  1 X^2  1 X^2+X  1  1  X X^2+X  1  1  1 X^2+X  1  X  X  1  1 X^2  1  1  1  1  X  X  0  1  1  1 X^2  1  1  X  1  0  1  0  1 X^2+X  X X^2+X  0  1  1 X^2  1  X  1  1  1  1  1
 0  1  0  0 X^2+1 X^2+1  1  X X^2  1  1 X^2+X  1 X+1  X  1 X^2 X^2+X+1 X^2+X  1  1  X  1  X X^2  1  1 X^2+1 X+1 X^2+X X^2+X+1  1 X^2+X  1 X+1 X^2+X X^2+1 X^2 X^2 X^2+X+1  1 X^2  1 X^2  1 X^2  1  1  1  1  X X+1  X X^2+X+1 X^2  X X+1 X^2 X^2  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X X^2+1  1  1  0 X^2  0  1  1  X  1 X^2+1  0  X X+1  1 X+1 X^2+X+1 X^2  X  0 X+1 X^2+1  1  1 X^2+X X^2+X X^2  X  1  0 X^2+X+1 X^2+X X^2+1 X+1 X^2+X  X  1 X^2+X X^2+X X+1 X^2+1 X^2+X+1  1  1 X+1  1 X^2 X^2 X^2  X  0
 0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  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+30x^56+204x^57+206x^58+252x^59+32x^60+32x^61+22x^62+16x^63+23x^64+84x^65+58x^66+52x^67+8x^68+2x^70+2x^72

The gray image is a linear code over GF(2) with n=240, k=10 and d=112.
This code was found by Heurico 1.16 in 0.124 seconds.