The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^60+8x^62+3x^64+2x^76

The gray image is a linear code over GF(2) with n=240, k=6 and d=120.
As d=120 is an upper bound for linear (240,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.0549 seconds.