The generator matrix

 1  0  1  1  1  1  1
 0  1 16 21  4 26 24

generates a code of length 7 over Z27 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+140x^12+12x^13+288x^14+278x^15+6x^16+4x^18

The gray image is a code over GF(3) with n=63, k=6 and d=36.
This code was found by Heurico 1.16 in 0.000214 seconds.