The generator matrix
1 0 1 1 1 1 1 0 1 1 1 X 1 1 1 X 1 1 1 0 1 1 1 X 1 1 1 1 1 1 2X 2X 1 1 1 2X 1 1 1 1 0 1 1 0 1 1 1 X 1 1 1 X 1 1 1 1 1 1 0 X 1 1 1 1 1 1 1 1 1 2X 2X 2X 1 X X X X X X X 1 1 1
0 1 1 2 2X+1 0 2 1 X 2X+1 X+2 1 X X+1 X+2 1 X+1 0 2 1 X 1 X+2 1 2X 2X 2X+1 X+1 2X+2 2X+2 1 1 2X 1 2X+2 1 0 2X+1 2 0 1 2X+1 2 1 X X+1 X+2 1 X X+1 X+2 1 X+1 2X+1 0 X 2 X+2 1 1 2X 2X 2X 1 1 1 2X+2 2X+2 2X+2 1 1 1 0 0 X X 0 2X 2X X X 2 0
0 0 2X 0 X X 2X 2X 2X 0 X X X 2X 2X 2X X 2X X X 0 0 0 0 0 X 2X 0 X 2X 0 X 2X X 0 2X 0 2X 0 2X X X X 0 X 0 2X 2X 2X X X X 2X 0 X 0 2X 0 2X 0 0 X 2X 2X X 0 0 X 2X 0 X 2X 0 X 2X X 2X X 2X 0 0 0 X
generates a code of length 83 over Z3[X]/(X^2) who´s minimum homogenous weight is 164.
Homogenous weight enumerator: w(x)=1x^0+102x^164+22x^165+30x^167+42x^168+12x^170+8x^171+18x^173+8x^174
The gray image is a linear code over GF(3) with n=249, k=5 and d=164.
This code was found by Heurico 1.16 in 0.0843 seconds.