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

generates a code of length 89 over Z27 who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+84x^169+18x^170+56x^171+618x^172+144x^173+120x^174+60x^175+918x^176+198x^177+1548x^178+1548x^179+238x^180+270x^181+288x^182+96x^183+42x^184+18x^186+24x^187+228x^190+42x^193+2x^252

The gray image is a code over GF(3) with n=801, k=8 and d=507.
This code was found by Heurico 1.16 in 1.02 seconds.