The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  0  X X^2 X^2+X X^2+X X^2 X^2  X  0 X^2+X  0  X  0 X^2+X  0  X  0 X^2+X X^2+X X^2  0  X  X  0 X^2  0 X^2 X^2+X X^2+X  X X^2+X  X X^2+X X^2 X^2 X^2  0 X^2  0 X^2+X  X  X  0 X^2 X^2+X X^2+X  0 X^2+X
 0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0
 0  0  0 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2  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  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 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+67x^54+65x^56+235x^58+235x^60+256x^61+33x^62+34x^64+49x^66+48x^68+1x^116

The gray image is a linear code over GF(2) with n=240, k=10 and d=108.
This code was found by Heurico 1.16 in 0.209 seconds.