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.