The generator matrix

 1  0  0  1  1  1 15  1  1  1  3  1 21  1  1  1  1
 0  1  0  1 15 26  1 19 20 18  1 17  0 22 15 15  3
 0  0  1 26 16 26 22 19 21 20 23 19  1 18 24 11 25
 0  0  0 24 15  9  3 21  3  6 12 15  6  3  0 24 24

generates a code of length 17 over Z27 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+402x^27+1584x^28+594x^29+7302x^30+8532x^31+16848x^32+26556x^33+42336x^34+32562x^35+26704x^36+11700x^37+1026x^38+942x^39+48x^42+10x^45

The gray image is a code over GF(3) with n=153, k=11 and d=81.
This code was found by Heurico 1.16 in 32.7 seconds.