The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  X  1 X^2+X  1  1  1  X  1  X  1 X^2  1  1  0  1  0 X^2+X  1  0  1  1  1  X  1  1  1  0 X^2+X  1  1  1  0  1  1 X^2 X^2+X  0  1 X^2+X  1  1  1 X^2  1  1  1  1  1  1
 0  1  0  0  1 X^2+X+1  1 X^2  0 X^2 X^2+X+1  1 X^2+X+1  1  0 X+1  X  1  1  0  0  1  X X+1  X X^2+1  1  X X+1  1 X^2+X X+1 X^2  1 X^2+X+1 X^2+X+1 X^2  1  X X^2  0 X^2  1 X^2+X X^2+X  1  0  1 X^2+1  1  X X^2+X  0  1  1  X X^2 X+1  0  0
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  X  1 X^2+X+1 X+1  0 X^2  X  1 X^2+X X^2+X+1 X^2+X+1 X^2+1  1  0  0  1  1 X^2+1 X^2+X X+1 X^2+X X^2+X+1 X^2+X+1  0  1 X^2+X  1  1 X^2+X X+1  1  1 X^2+1  1  1  X X+1 X+1 X^2+X X^2 X^2+1 X^2  0 X^2+1  0  X X^2+1  0
 0  0  0  X  X X^2+X X^2 X^2+X  0  0  X X^2  0 X^2+X X^2 X^2  X  X X^2 X^2+X X^2+X  0  0 X^2 X^2+X  X X^2+X  0 X^2+X  X X^2 X^2+X X^2  0  0 X^2  0  X X^2  X X^2+X  0  0  0 X^2+X X^2+X X^2 X^2+X  0  0 X^2+X X^2 X^2 X^2+X  X X^2+X  X  X  0  0
 0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0
 0  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0  0 X^2 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 52.

Homogenous weight enumerator: w(x)=1x^0+56x^52+194x^53+261x^54+504x^55+543x^56+776x^57+680x^58+882x^59+665x^60+898x^61+549x^62+678x^63+444x^64+412x^65+257x^66+188x^67+73x^68+48x^69+40x^70+14x^71+8x^72+8x^73+3x^74+6x^75+2x^76+2x^78

The gray image is a linear code over GF(2) with n=240, k=13 and d=104.
This code was found by Heurico 1.16 in 3.07 seconds.