The generator matrix

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

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+168x^52+88x^53+412x^54+316x^55+694x^56+472x^57+944x^58+660x^59+926x^60+656x^61+738x^62+484x^63+657x^64+312x^65+320x^66+76x^67+138x^68+8x^69+64x^70+32x^72+16x^74+8x^76+2x^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 4.01 seconds.