The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+24x^58+64x^59+76x^60+64x^61+22x^62+3x^64+2x^86

The gray image is a linear code over GF(2) with n=240, k=8 and d=116.
This code was found by Heurico 1.16 in 0.0869 seconds.