The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+35x^52+182x^53+276x^54+642x^55+405x^56+826x^57+620x^58+972x^59+493x^60+1010x^61+541x^62+712x^63+395x^64+462x^65+196x^66+216x^67+67x^68+72x^69+30x^70+14x^71+7x^72+8x^73+4x^75+5x^76+1x^78

The gray image is a linear code over GF(2) with n=240, k=13 and d=104.
This code was found by Heurico 1.16 in 3.09 seconds.