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 1 1 X 1 1 1 X 1 1 1 X 1 1 2X 1 1 X 1 1 1 1 1 1 1 2X 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 2X 1 1 X 1 1 0 1 X 0 1 2X 1 1 X 1 1 1 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 X X+1 1 2 X+1 2X 1 1 0 2X+2 1 X+1 1 1 2X+2 X+2 1 2X X X+1 2 2X+1 2X+1 2X+2 1 2X+1 1 X+1 2X 2X+1 2X+1 X+2 0 2X X+1 X+1 X+1 X 2X+2 X+2 1 2 X+2 1 X+2 2 1 1 1 X 0 1 2 X 1 X+2 X 2X 2X+2 X+2 X
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 X X 0 2X X X 0 2X 0 X X 2X 2X X 2X 0 X 0 0 0 2X 2X X X X 0 0 0 2X 2X 0 X 0 X X 2X X X 2X 0 0 2X 2X 0 0 0 2X X 2X X 0 X X 0 X X 0 2X 2X X 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 X 2X 0 0 2X 0 0 0 2X 2X 0 X 2X 2X X 0 2X 2X 0 X 0 X 0 0 2X 0 0 2X 2X 2X 0 X X 2X 0 2X 0 2X X 2X 2X 0 0 X 2X 0 0 2X 0 X X X X 2X X 0 2X 2X X 2X
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 2X X 2X X 0 X X 2X X 0 X 2X X X 0 X X 0 X X X X 0 2X 0 X 2X 2X X X 0 0 X 0 0 0 2X 0 0 0 X 2X X 2X X 2X X 0 X X 2X 0 X 2X 0 2X X 2X 2X X 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 X 0 0 2X 0 2X X 0 2X 2X X 2X X 0 2X X X X X 0 2X 0 0 2X 0 X X 0 0 2X X 0 0 X 0 2X 2X X X X 0 X X 0 2X 2X X 2X 0 2X 0 0 X X X X X 0 2X 0 0
generates a code of length 89 over Z3[X]/(X^2) who´s minimum homogenous weight is 165.
Homogenous weight enumerator: w(x)=1x^0+112x^165+186x^166+252x^168+498x^169+280x^171+636x^172+338x^174+492x^175+280x^177+702x^178+264x^180+648x^181+174x^183+594x^184+170x^186+354x^187+146x^189+228x^190+54x^192+24x^193+42x^195+12x^196+30x^198+16x^201+8x^204+4x^207+2x^210+4x^213+4x^216+4x^219+2x^228
The gray image is a linear code over GF(3) with n=267, k=8 and d=165.
This code was found by Heurico 1.16 in 1.16 seconds.