The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  X  1 X^2  1  1  1  1  0  1  1 X^2+X  1  1  1  X  1 X^2+X  1  1  1  0 X^2+X  X  1  1  1 X^2+X  1 X^2+X X^2  1  1  1 X^2  1  1  1  X  X  0  1 X^2+X  1  1 X^2+X  X  1  1  X X^2
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1  1  0 X^2+X+1 X^2 X^2+X+1  1  X  1  1  X X^2+1 X^2+1  1  0  1 X^2+X+1 X^2+X+1 X^2  1  1  1  X X^2+1 X^2+X  1  1  1  1 X^2+X+1  0 X+1  1 X+1  0 X^2+X  1 X^2  0  X  1  X  1  1  0 X+1  X  0  1
 0  0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2+X  X X^2  X X^2  X  X X^2 X^2  X  X  0 X^2 X^2 X^2 X^2+X  0  0  X  X  X X^2  0 X^2+X  X X^2+X X^2  X X^2+X  0  X X^2+X X^2  0 X^2+X  0 X^2  0 X^2+X X^2+X  X X^2+X X^2+X X^2+X  0  0 X^2+X X^2 X^2  X X^2+X
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  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+139x^50+12x^51+405x^52+100x^53+886x^54+352x^55+1433x^56+672x^57+2110x^58+888x^59+2432x^60+936x^61+2094x^62+704x^63+1449x^64+320x^65+760x^66+92x^67+353x^68+20x^69+134x^70+57x^72+14x^74+10x^76+6x^78+4x^80+1x^82

The gray image is a linear code over GF(2) with n=240, k=14 and d=100.
This code was found by Heurico 1.16 in 41 seconds.