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

generates a code of length 89 over Z27 who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+146x^174+536x^177+972x^178+510x^180+16x^183+4x^186+2x^261

The gray image is a code over GF(3) with n=801, k=7 and d=522.
This code was found by Heurico 1.16 in 0.441 seconds.