The generator matrix

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

generates a code of length 88 over Z3[X]/(X^2) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+102x^165+144x^166+282x^167+500x^168+402x^169+372x^170+498x^171+300x^172+300x^173+356x^174+294x^175+252x^176+334x^177+234x^178+246x^179+262x^180+180x^181+186x^182+184x^183+162x^184+114x^185+160x^186+120x^187+84x^188+160x^189+54x^190+66x^191+48x^192+30x^193+36x^194+50x^195+18x^196+12x^198+6x^199+6x^200+6x^204

The gray image is a linear code over GF(3) with n=264, k=8 and d=165.
This code was found by Heurico 1.16 in 0.885 seconds.