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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+334x^56+128x^58+128x^60+128x^62+286x^64+18x^72+1x^96

The gray image is a linear code over GF(2) with n=240, k=10 and d=112.
This code was found by Heurico 1.16 in 78.4 seconds.