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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+20x^57+88x^58+32x^59+24x^60+60x^62+7x^64+8x^65+8x^66+4x^70+4x^73

The gray image is a linear code over GF(2) with n=240, k=8 and d=114.
This code was found by Heurico 1.16 in 8.34 seconds.