The generator matrix

 1  1  1  1  1  1  1  3  1  3  1  1  1  3  1
 0  3 24  0 21 24  0 21 21 24 24  0  9 21  0
 0  0  9  0  0  0  0 18 18 18 18 18  0  9  0
 0  0  0  9  0  0  9 18 18  0  0  9  0 18 18
 0  0  0  0 18  0 18 18 18  0 18  0  9  9 18
 0  0  0  0  0  9 18  0  9  9 18 18  9 18  9

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

Homogenous weight enumerator: w(x)=1x^0+90x^21+406x^24+486x^26+1394x^27+1458x^28+1944x^29+6918x^30+2916x^31+1944x^32+1834x^33+234x^36+48x^39+10x^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 3.19 seconds.