The generator matrix

 1  0  0  1  1  1 15  1  1  3  1  1  1  3  1
 0  1  0  1 15 26  1 19 20  1 18 24 10  6 18
 0  0  1 26 16 26 22 19 21 23 20 16 24  3  2
 0  0  0 24 15  9  3 21  3 12  6  0  6 15 12

generates a code of length 15 over Z27 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+144x^23+1734x^24+1794x^25+5136x^26+8328x^27+23358x^28+19638x^29+37378x^30+45144x^31+20070x^32+11422x^33+2562x^34+210x^35+176x^36+42x^37+8x^39+2x^42

The gray image is a code over GF(3) with n=135, k=11 and d=69.
This code was found by Heurico 1.16 in 441 seconds.