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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 173.

Homogenous weight enumerator: w(x)=1x^0+330x^173+218x^174+294x^176+158x^177+282x^179+126x^180+234x^182+64x^183+114x^185+44x^186+78x^188+40x^189+36x^191+46x^192+36x^194+14x^195+12x^197+2x^198+6x^200+14x^201+24x^203+6x^206+2x^207+6x^209

The gray image is a linear code over GF(3) with n=270, k=7 and d=173.
This code was found by Heurico 1.16 in 45.9 seconds.