The generator matrix

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

generates a code of length 15 over Z27 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+52x^21+18x^22+72x^23+260x^24+144x^25+234x^26+782x^27+1854x^28+486x^29+10066x^30+3600x^31+468x^32+1016x^33+180x^34+198x^35+198x^36+36x^37+16x^39+2x^42

The gray image is a code over GF(3) with n=135, k=9 and d=63.
This code was found by Heurico 1.16 in 0.272 seconds.