The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+66x^53+167x^54+254x^55+328x^56+386x^57+357x^58+360x^59+404x^60+344x^61+357x^62+330x^63+263x^64+202x^65+95x^66+62x^67+40x^68+22x^69+12x^70+16x^71+18x^72+2x^73+4x^74+2x^75+2x^80+2x^81

The gray image is a linear code over GF(2) with n=240, k=12 and d=106.
This code was found by Heurico 1.16 in 0.865 seconds.