The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+76x^50+240x^51+451x^52+770x^53+1210x^54+1544x^55+1976x^56+2336x^57+2811x^58+3346x^59+3292x^60+3218x^61+2988x^62+2518x^63+1967x^64+1468x^65+1020x^66+610x^67+415x^68+250x^69+134x^70+58x^71+24x^72+20x^73+11x^74+4x^75+2x^76+2x^77+4x^78+2x^82

The gray image is a linear code over GF(2) with n=240, k=15 and d=100.
This code was found by Heurico 1.16 in 42.1 seconds.