The generator matrix

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

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+121x^54+346x^55+324x^56+402x^57+384x^58+492x^59+272x^60+444x^61+284x^62+314x^63+193x^64+168x^65+145x^66+56x^67+33x^68+52x^69+25x^70+24x^71+8x^72+6x^73+1x^74+1x^76

The gray image is a linear code over GF(2) with n=240, k=12 and d=108.
This code was found by Heurico 1.11 in 0.25 seconds.