The generator matrix

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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+136x^171+48x^172+108x^173+258x^174+204x^175+90x^176+234x^177+114x^179+142x^180+66x^181+48x^182+126x^183+78x^184+36x^185+114x^186+30x^188+84x^189+48x^190+42x^191+42x^192+42x^193+18x^194+60x^195+4x^198+4x^201+4x^204+2x^207+2x^210+2x^213

The gray image is a linear code over GF(3) with n=270, k=7 and d=171.
This code was found by Heurico 1.16 in 0.23 seconds.