The generator matrix

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

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+174x^50+390x^51+1024x^52+1528x^53+2389x^54+2904x^55+4158x^56+4586x^57+6040x^58+5848x^59+7077x^60+6230x^61+6164x^62+4588x^63+4489x^64+2798x^65+2220x^66+1326x^67+794x^68+386x^69+207x^70+100x^71+54x^72+24x^73+22x^74+12x^75+1x^76+2x^80

The gray image is a linear code over GF(2) with n=240, k=16 and d=100.
This code was found by Heurico 1.13 in 46.3 seconds.