The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^2  0  0  X  1  1  X  0  1  X  0  X  1  X  1  1  0 X^2  1  X  X  X  X  X  1  1  X  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2 X^2  0  X X^2 X^2+X  X  0 X^2 X^2  X  0  X X^2+X X^2 X^2+X  0 X^2  X  X X^2 X^2  X  0 X^2+X  X X^2  X  X  X  0  X  0  X  0  0  X  0 X^2 X^2+X  X  X X^2+X  0 X^2  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0  0  X X^2+X X^2+X X^2+X  0 X^2  X X^2+X X^2+X X^2+X  X X^2 X^2+X  X X^2+X  0  0  X X^2+X X^2+X X^2  0 X^2  0 X^2+X  X X^2 X^2 X^2 X^2+X  0 X^2  0 X^2+X  X  X  X X^2  X X^2 X^2+X  X  0  0  X  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  0  X X^2+X  0  0 X^2+X  X X^2  X  0 X^2 X^2  0  X  X  0  X  0 X^2  0 X^2  X  0  X X^2+X  X X^2+X  X  0  X X^2+X  X  X X^2 X^2  X X^2 X^2 X^2  0  X  0  0  0  0  X X^2+X
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2+X  0  X X^2+X X^2 X^2  0 X^2+X  X  0  0  X X^2+X  0 X^2 X^2+X X^2  0  0  X  0  X  X  X X^2  X  0  X  X X^2+X X^2+X X^2  0 X^2 X^2 X^2  X  X  0 X^2 X^2+X X^2+X X^2  X X^2+X X^2+X
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 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+57x^50+108x^51+144x^52+242x^53+356x^54+400x^55+416x^56+626x^57+702x^58+710x^59+746x^60+722x^61+783x^62+576x^63+403x^64+354x^65+254x^66+200x^67+108x^68+84x^69+74x^70+48x^71+36x^72+20x^73+10x^74+6x^75+2x^76+3x^78+1x^82

The gray image is a linear code over GF(2) with n=240, k=13 and d=100.
This code was found by Heurico 1.16 in 5.06 seconds.