The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  1  1  1  1  1  1  1  1  0  1  1  0  0  3  1  3  3  1  0  3
 0  3  0  0 24 21  3 15 24  0  9 18 21 21  6  3 15  6 15 18  3 18  3  9 24  3  6 12 21  9  0  0 21 24  9  6  9 24  6 12 15 21  0  6  6  0  3 21  3  9 15 24 24  9 21  9 12  0 12 18 21  0 18  9  6  9 12 24  9 24 12  9 24 12 12 21  3 15  3 12  0  9  3 24  9 24 18  3  3 24
 0  0  3 24  0 15  3 21 24 18 15 21 15 18  0  3 21 24  9 15 12 21  9 18 24 24  3  3 24  0  3 15  9 15  6 21  0 18 21  9 12  3 21  6 21  9  9  6 21  6 15 15  0  9  9 21  3  3  3  6 18 21  3  6 24 24  6 18  9 12 21  9  0  6  9 24 15 15 24  0  3  3  0 18  3 15 24  6 15 24
 0  0  0  9  0  0  0  0  0  0  0 18 18  9 18  9 18 18  9 18 18  9 18 18 18  9  9  0 18  0  0 18  0 18  0 18  9 18 18  0  0  9  9  9  9  9 18  0 18  9  0  0  0  9 18  0  0 18 18 18  0 18  9  0  9  9  9  0 18  0  9 18  9  9  9  9  0  9  0  9  9  9 18  9  0 18  0  9 18  0
 0  0  0  0  9 18  9 18  0 18  9  9  0 18 18  0  0  9  0 18 18 18  9 18 18  0  0 18 18  9  9  9  9  0 18  9 18  9 18 18  0  9  9  9 18  0  0  9  9  9  9 18  0  9 18 18  0 18  0  0 18  0  0  0 18 18 18  0  0  9 18  9 18  0  0  9  0  0 18  9  9  0  9  0  0  9  9 18  0  9

generates a code of length 90 over Z27 who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+198x^169+378x^170+36x^171+528x^172+618x^173+108x^174+810x^175+1026x^176+142x^177+3438x^178+2112x^179+138x^180+4836x^181+1782x^182+174x^183+1140x^184+774x^185+88x^186+240x^187+240x^188+30x^189+210x^190+150x^191+6x^192+108x^193+120x^194+4x^195+84x^196+60x^197+60x^199+24x^200+12x^202+6x^203+2x^243

The gray image is a code over GF(3) with n=810, k=9 and d=507.
This code was found by Heurico 1.16 in 7.94 seconds.