The generator matrix

 1  0  0  1  1  1  0  1  1  1 X^2+X  1  0 X^2  1  1  1 X^2+X  1  X  X  X  1  1 X^2+X  1 X^2  1  1 X^2+X  X  1  1  0  1 X^2  1  1 X^2+X X^2+X  0  1 X^2  0  X  1  1  1  1  X  1  X  1  1  1  1  1  1  1  1
 0  1  0  0  1  1  1 X^2 X^2+X+1 X+1  1  X  1 X^2+X X^2+X X^2+X+1 X^2+X  1  1 X^2+X  1 X^2 X+1  X  1 X^2  1 X^2+1 X^2+1 X^2  1 X^2+X+1  X  1 X^2  1 X^2+X+1  X  0  1 X^2+X  0  1  1  1  X X^2+X+1 X^2+X X+1  1 X^2+X  X X^2+1  1  1  X X^2+X  X X^2+1 X^2+1
 0  0  1 X+1 X^2+X+1  0 X+1  X X^2+X X^2+X+1 X^2+X+1 X^2+1 X^2+X  1 X^2  1 X+1 X^2  X  1  1  1  0  X X^2+X  1  1  1 X^2+1  1 X^2+X+1  0  1 X^2+X+1  0 X^2+X X+1 X+1  1  0  1 X+1  0 X^2+X+1 X^2+X X^2+X X+1  1  1 X+1  1  1 X^2  X  X X^2+X+1 X^2  0  1 X+1
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 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  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0 X^2  0  0  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  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 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 54.

Homogenous weight enumerator: w(x)=1x^0+139x^54+260x^55+388x^56+424x^57+394x^58+428x^59+400x^60+376x^61+266x^62+276x^63+223x^64+136x^65+120x^66+116x^67+64x^68+24x^69+35x^70+8x^71+12x^72+6x^74

The gray image is a linear code over GF(2) with n=240, k=12 and d=108.
This code was found by Heurico 1.16 in 0.708 seconds.