The generator matrix

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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+54x^172+204x^173+200x^174+150x^175+228x^176+204x^177+78x^178+174x^179+82x^180+78x^181+120x^182+76x^183+18x^184+102x^185+54x^186+30x^187+60x^188+54x^189+48x^190+42x^191+22x^192+18x^193+6x^194+6x^195+12x^197+26x^198+12x^200+12x^202+6x^203+6x^206+2x^210+2x^216

The gray image is a linear code over GF(3) with n=270, k=7 and d=172.
This code was found by Heurico 1.13 in 0.188 seconds.