The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+164x^51+543x^52+744x^53+1185x^54+1614x^55+2272x^56+2228x^57+3054x^58+2846x^59+3479x^60+3002x^61+2968x^62+2398x^63+2134x^64+1520x^65+1192x^66+616x^67+438x^68+178x^69+95x^70+40x^71+25x^72+8x^73+14x^74+2x^75+4x^76+4x^78

The gray image is a linear code over GF(2) with n=240, k=15 and d=102.
This code was found by Heurico 1.16 in 37.3 seconds.