The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 0 1 1 1 1 1 2X 1 X 1 X 1 1 1 2X 1 1 1 1 0 1 X 1 1 1 1 1 1 0 1 X 1 X 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2X 1 1 1 1 1 1 X 1 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 X+1 1 0 2 2X+1 X+1 2 1 X+2 1 2 1 0 X+2 X 1 X 1 X 2X+1 1 2X 1 2X+2 X 2X 1 0 2X+2 1 2X+2 1 X+2 1 1 2X+2 2 X+1 1 X 0 2X 2X+1 0 2X+1 2X+1 X+2 X 2X+2 X X+1 2X+2 0 1 X+2 X+2 X+2 X+1 2X+1 X+2 1 2X+1 X+1 1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 0 X X 2X 0 X X X 0 2X 2X 2X X X 0 0 X X 2X X 0 0 0 X 2X X 0 2X X 2X X 0 2X 0 2X 2X 0 2X 0 X X X 2X X X X X 0 X 2X 0 0 2X X 0 2X X 0 0 2X 0 0 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 2X 2X 2X 2X X X X 2X 0 X 0 X 2X 2X X 2X 2X 2X X 2X 2X X X X 2X 0 X X 2X 2X X 0 X 2X 2X 2X X X X 2X 2X X X 0 2X 0 2X 2X 2X 0 2X 0 X X 2X 2X 2X 0 X X X 2X 0 X
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 X X 2X 0 X 0 2X 2X X X X 2X X 0 X 2X 0 0 0 X X X 2X 0 X 0 X 2X 0 0 X 2X 2X X 2X 0 X X 0 X 2X 0 2X 2X 0 0 X 0 X 2X 0 X X 2X 2X 2X X 2X X 2X X X 2X 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 X X 0 0 2X 0 X 2X 2X 2X 2X 0 X 0 0 X 2X 2X 2X X 0 X X 2X 2X 0 0 0 0 2X 2X 2X X 2X X X X 2X X 2X X X 0 0 0 0 X 2X 0 0 X X X X 2X X X 0 X X X 2X 0
generates a code of length 83 over Z3[X]/(X^2) who´s minimum homogenous weight is 153.
Homogenous weight enumerator: w(x)=1x^0+80x^153+192x^154+278x^156+366x^157+260x^159+654x^160+396x^162+600x^163+240x^165+708x^166+216x^168+744x^169+224x^171+564x^172+200x^174+330x^175+142x^177+168x^178+66x^180+48x^181+20x^183+20x^186+10x^189+12x^192+10x^195+6x^198+4x^201+2x^210
The gray image is a linear code over GF(3) with n=249, k=8 and d=153.
This code was found by Heurico 1.16 in 1.06 seconds.