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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  X  0  X  X 2X 2X 2X  X  0  X  X  X  X 2X 2X 2X 2X  X  0  0  0  0 2X  0 2X  0  X  0  X  X 2X 2X 2X  X  X  0  0  X  X 2X 2X  0  X 2X  0  X 2X 2X  0  0 2X  0  X 2X 2X  X 2X  X  0  X  0  X 2X 2X 2X  0  0  X  X  0  X 2X 2X
 0  0  X  0  0  0  X  0  X 2X  X  X  0  X  X  X  0  0  X  X 2X  0  0  X  X 2X  X  0  0  0 2X  X 2X 2X 2X 2X 2X 2X 2X 2X  X  0  0  X  X  0  0  X  X  0  X  0  0  X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  X 2X 2X  X  0  X 2X  0  X 2X  X 2X  0  0  X
 0  0  0  X  0  X 2X 2X 2X  X  0  0  0  0 2X  X  X  X  0 2X  X  X  X 2X  X  X  0 2X 2X 2X  X 2X 2X  0  0 2X 2X  X 2X 2X 2X  0  0  X  X 2X  0  X  0  0  0  X  X 2X  0  0  X 2X 2X  X  0 2X 2X  0  X 2X  0 2X  0  X  X  X 2X  X  0  X  0 2X 2X  X
 0  0  0  0  X 2X  X  X 2X 2X 2X  0  X 2X 2X  0  0  X  X  0  X  0 2X  0  X  X  X  0 2X  X 2X 2X  X  0 2X 2X  0  0  0  X  X  X 2X  X 2X  0 2X 2X 2X 2X  X  X 2X  X  X  X  0 2X  0  X  0 2X  X  0  0  0 2X 2X  0  X  0 2X  X 2X  X  0  0 2X  0  X

generates a code of length 80 over Z3[X]/(X^2) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+160x^159+486x^160+80x^162+2x^240

The gray image is a linear code over GF(3) with n=240, k=6 and d=159.
As d=159 is an upper bound for linear (240,6,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.114 seconds.