The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+110x^51+552x^52+896x^53+1219x^54+1608x^55+1982x^56+2392x^57+2797x^58+3282x^59+3104x^60+3182x^61+3031x^62+2364x^63+2115x^64+1564x^65+1087x^66+722x^67+384x^68+176x^69+82x^70+68x^71+22x^72+12x^73+8x^74+6x^75+2x^77

The gray image is a linear code over GF(2) with n=240, k=15 and d=102.
This code was found by Heurico 1.13 in 12.3 seconds.