The generator matrix

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

generates a code of length 16 over Z27 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+24x^21+24x^23+76x^24+240x^26+336x^27+486x^28+960x^29+3340x^30+1944x^31+1758x^32+6616x^33+1944x^34+1272x^35+430x^36+120x^38+88x^39+4x^42+16x^45+4x^48

The gray image is a code over GF(3) with n=144, k=9 and d=63.
This code was found by Heurico 1.16 in 0.274 seconds.