The generator matrix

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

generates a code of length 89 over Z27 who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+120x^168+726x^170+784x^171+1968x^173+1366x^174+2424x^176+1918x^177+3144x^179+2130x^180+2508x^182+1410x^183+654x^185+202x^186+144x^188+40x^189+78x^191+24x^192+18x^194+8x^195+2x^198+6x^201+2x^204+4x^207+2x^210

The gray image is a code over GF(3) with n=801, k=9 and d=504.
This code was found by Heurico 1.16 in 1.88 seconds.