The generator matrix

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

generates a code of length 12 over Z27 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+54x^20+60x^21+180x^22+36x^23+1578x^24+72x^25+36x^26+60x^27+72x^28+36x^29+2x^36

The gray image is a code over GF(3) with n=108, k=7 and d=60.
This code was found by Heurico 1.16 in 0.00384 seconds.