The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+202x^53+331x^54+580x^55+438x^56+856x^57+578x^58+986x^59+490x^60+928x^61+551x^62+832x^63+351x^64+474x^65+204x^66+180x^67+58x^68+62x^69+54x^70+12x^71+6x^72+4x^73+9x^74+2x^75+2x^81+1x^82

The gray image is a linear code over GF(2) with n=240, k=13 and d=106.
This code was found by Heurico 1.16 in 30.2 seconds.