The generator matrix

 1  0  1  1  1  1 21  1  1  1 24  1  1  1 21  1  3  1  1  1  1 24  1  1 18  1  1  1  1 15  1  1  1  1  1  1  1  1 18  1  1  6  0  1  1  1 15  1  1  1  1  1  1  1  6  1  1  1 15  1  1  1  3  1  1  1  1  1  1  1  1  1  0 18  1  1  1  1  1  1  1  1  1  3  1  1  1 18 12  1
 0  1  1 26 21 20  1 16 23 24  1  4 19  0  1 17  1 20 16 24 23  1  3  4  1 21 25 14 15  1  2  4 26 25 24 16 18 11  1 21 20  1  1 21  5  4  1 26 22 11 23 16  8 17  1  9 26  4  1  0  8 13  1  8  3  6  4 11 25 22 18 12  1  1 19  3 22 19 10 13 24 18 12  1 25  8  0  1  1 18
 0  0 24  0  0 18 18 18  0  9  0 18 18 15 15 21 21 24 24 15 15  6 21 15  3 24 21 12 12 21 12  6  6 21  9 24  3 18 21  9 15  6 15  6 18  0 21 12 12 21  6  9  9  3  3  3  6 24  6  0  0  0  9 15  3  0  3 24 24  9 18  3  3  6  3 15 24  0 18  9  3  0  6  3 18 12  0  9 24 12
 0  0  0  9  0  0  0 18 18  0  0  9 18  0  0  9 18  9 18  9 18  9  9 18  9  9  0 18 18  0  9 18  9  0  9  0  0  0 18 18  9  9  0  9  9 18  9 18  0  9  0  9  9 18  0 18 18  0 18  9 18  0 18  0  0  9  9  9 18  0 18  9  9  9 18  9  0 18 18  9  0  0 18  9  0 18  9  9  0  0
 0  0  0  0 18 18  9  9  9  9 18  0  0  9 18  9  9 18  0 18  9  9  0 18  0  9 18  0  9 18  0  9  9  9  9  9  0  9 18  0  0 18  9  0  9 18  9 18  0 18  0  9 18  9  0  0  0  0  9  0  0  9 18  0  0 18  0  9 18  0 18  9 18 18  0  0  9  0 18  9 18  9 18  9  9  0  9 18  0 18

generates a code of length 90 over Z27 who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+60x^168+192x^169+270x^170+756x^171+1488x^172+1698x^173+2178x^174+2850x^175+3396x^176+3952x^177+4428x^178+4608x^179+5436x^180+5658x^181+5226x^182+4708x^183+3924x^184+2940x^185+2026x^186+1398x^187+642x^188+364x^189+234x^190+72x^191+104x^192+120x^193+60x^194+54x^195+84x^196+18x^197+18x^198+18x^199+6x^200+6x^201+18x^202+12x^203+10x^204+6x^206+2x^207+4x^210+2x^216+2x^219

The gray image is a code over GF(3) with n=810, k=10 and d=504.
This code was found by Heurico 1.16 in 14.1 seconds.