The generator matrix

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

generates a code of length 89 over Z27 who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+420x^165+678x^166+3348x^167+5806x^168+7188x^169+11052x^170+16512x^171+17694x^172+25302x^173+29634x^174+31104x^175+39804x^176+46940x^177+43662x^178+46494x^179+47594x^180+38262x^181+36648x^182+30580x^183+17766x^184+14874x^185+9684x^186+5064x^187+2892x^188+1430x^189+360x^190+312x^191+110x^192+36x^193+36x^194+42x^195+12x^196+24x^197+46x^198+6x^199+6x^201+6x^202+6x^203+6x^204

The gray image is a code over GF(3) with n=801, k=12 and d=495.
This code was found by Heurico 1.16 in 780 seconds.