The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  7  3  1 17  0
 0  0  1 14  2  1 21  0
 0  0  0  9 18  0 18  9

generates a code of length 8 over Z27 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+138x^10+48x^11+1228x^12+828x^13+5958x^14+4848x^15+28062x^16+11916x^17+4844x^18+1104x^19+60x^20+8x^21+6x^24

The gray image is a code over GF(3) with n=72, k=10 and d=30.
This code was found by Heurico 1.16 in 0.302 seconds.