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  1  1  1  1  1  1  1  1  1  1  1  1  1  X  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  0 X^2+X X^2  X  0 X^2+X X^2  X  0 X^2+X X^2 X^2+X  0 X^2+X X^2 X^2+X X^2 X^2+X X^2  X X^2 X^2+X X^2  X  0 X^2 X^2+X  X X^2 X^2+X  0  X X^2  X  0 X^2 X^2 X^2+X  X  X  0 X^2+X X^2+X  0
 0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0
 0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  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+16x^56+8x^57+25x^58+120x^59+168x^60+120x^61+35x^62+8x^63+7x^64+3x^66+1x^118

The gray image is a linear code over GF(2) with n=240, k=9 and d=112.
This code was found by Heurico 1.16 in 0.133 seconds.