The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1 15 26 19 18
 0  0  1 26 16 26 19 15
 0  0  0 24 15  9 21 12

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

Homogenous weight enumerator: w(x)=1x^0+306x^10+264x^11+3118x^12+1836x^13+23454x^14+12408x^15+73656x^16+46908x^17+12404x^18+2448x^19+330x^20+8x^21+6x^24

The gray image is a code over GF(3) with n=72, k=11 and d=30.
This code was found by Heurico 1.16 in 2.48 seconds.