The generator matrix

 1  0  1  1  1  1  1  1
 0  1 16 26 21  4 20 24

generates a code of length 8 over Z27 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+150x^14+26x^15+234x^16+300x^17+16x^18+2x^21

The gray image is a code over GF(3) with n=72, k=6 and d=42.
This code was found by Heurico 1.16 in 0.000261 seconds.