The generator matrix

 1  0  0  0  1  1  1  1 X^2  1 X^2+X  X  1 X^2  1  1  1  X  1  1  X  0  1  0  X  1  1  0  1 X^2+X X^2+X  1  1  X  1 X^2 X^2  0  0  1  1  1  0  1  0 X^2+X  1  1  1  0  1  X  1  1  0 X^2  1  X  X  1
 0  1  0  0  0 X^2  1 X^2+1  1 X^2+X+1 X^2  1  0  1 X^2+1 X^2  1  1  X X+1  1  1 X^2 X^2+X X^2+X X^2+X+1  1 X^2+X X^2+X  1  X X^2+1  0  1  0  1  1  1  1 X^2+X X^2+X  0  X X^2+X  1  1 X^2+X X^2+X+1 X^2  1 X^2+X  1 X+1  X  1  1  1  1  1  0
 0  0  1  0  0 X^2+1  1 X^2+X X+1 X^2+1  1 X^2 X^2+X+1 X^2+1  X  X X^2+X+1 X^2+X+1 X^2 X^2 X+1 X^2+X X^2+1  1  1 X^2+X X^2+X+1 X^2+X X+1  0  1 X^2+X+1 X^2+X X^2+1  0 X^2+X  1 X^2+1  1 X+1 X^2+1  0  1  0 X+1  X  X X^2+X+1  1 X^2  X X^2  X X^2+X+1 X^2+X+1 X+1 X^2+X X^2+X+1  0 X^2+X
 0  0  0  1  1  1 X^2 X+1 X+1 X^2+1 X^2+1 X^2+1  X  X  0 X^2+1 X+1 X+1 X^2  X  0 X^2+X+1 X+1  1  X X^2+X+1 X^2+1  1  0 X^2+X X^2 X^2 X^2+X X^2+X  1  X X+1  X  1  0 X^2+X+1 X^2+X+1  1 X^2+X X^2+X  1  0 X^2  0  0  1  X X^2 X^2+1 X^2+1 X^2+X+1 X^2+X X^2+X X^2+X+1 X^2+1
 0  0  0  0  X  0  0  0  0  X  X  X X^2+X  X  X X^2+X  X X^2 X^2+X  0  0 X^2 X^2+X X^2 X^2+X  X  0 X^2+X  0 X^2+X X^2+X X^2+X  0 X^2 X^2 X^2 X^2  0 X^2+X X^2 X^2+X X^2  X  0 X^2+X X^2 X^2+X X^2  X X^2  0 X^2  X X^2+X X^2+X X^2+X  X X^2  X  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+152x^52+456x^53+566x^54+1130x^55+1044x^56+1384x^57+1170x^58+1646x^59+1380x^60+1690x^61+1190x^62+1484x^63+914x^64+930x^65+528x^66+374x^67+144x^68+80x^69+64x^70+30x^71+12x^72+2x^73+2x^74+8x^75+2x^77+1x^80

The gray image is a linear code over GF(2) with n=240, k=14 and d=104.
This code was found by Heurico 1.13 in 3.42 seconds.