The generator matrix

 1  0  0  1  1  1  1  1  1  1 18  1  3  1  1 12  1  1  9  1  1  1 12 12  1  1 24  1 18  1  1 15  1  1  1 12  1  1  3  1  1  9  1  1  1 12  1  1  1  1 24  1 21  1  1  9  1  1  1  1  1  1  1  1  1  1  1  1  1  1 15 12  1 24  1  1  1  1  1  0  1 21 18  1  1  1  1 12  9  1
 0  1  0  0  9 16 16 14  1 14  1 26  1 24  0 21 18 19  1 11 23 13  1  1 11 19  6 15  1  7  4  1  8 15  2  1 16  5  1 24 15  1 26 19 25  1 13  7 26 24  1 21 24 19 26  9  9 22  5 12 11 24 20 20  6 22  9 12 25 21  1  1 10  1  1 23 17 25 13  1 19  1  1 11 26  4 15  1  1  0
 0  0  1  1 17 17 15 16  7 21 16 23  2  4 23  1 18 18 19  5 21  2  3 17 13 10  1  7 16  1 18  8 22 23 26  1  2 24 18  9 20 21 25 19 20  7 14  3 26 20 14 18  1 13  2  1 17  9  4  4 24  1 21 17 23 25 20 22  5 21  8  7 23  6 24  6  2 20  7  9 21  5 25 19  3  7  3 24 10 18
 0  0  0 24 18  9  0  9  0 18 18  0  9  0  9  0 12 18 18  3 24 24  6 12 21 21 21  3 12  6 21 24 15  6 24 24 12 12 24 24 21 21  6 15 18  3  3 15 15  6 15  6  6  0  0 15  3 15 21 15 21  0 15 12 18  3 12 24 21 12 18  6 15  6 18  0 21  9  6  9 12  0 21  9 18  9  0 21 12 18

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

Homogenous weight enumerator: w(x)=1x^0+302x^168+372x^169+1470x^170+3392x^171+2946x^172+5946x^173+7652x^174+6792x^175+9828x^176+14120x^177+11106x^178+14232x^179+17022x^180+13506x^181+15036x^182+15960x^183+8946x^184+9696x^185+8202x^186+3558x^187+2952x^188+2166x^189+738x^190+426x^191+292x^192+84x^193+114x^194+80x^195+30x^196+60x^197+36x^198+36x^199+12x^200+18x^201+12x^204+6x^206

The gray image is a code over GF(3) with n=810, k=11 and d=504.
This code was found by Heurico 1.16 in 92.2 seconds.