The generator matrix

 1  0  1  1  1  1  1  1
 0  1  1 26  0 16 17  0
 0  0 24  0  9  6  6 21
 0  0  0  3 15 24 12 12

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

Homogenous weight enumerator: w(x)=1x^0+90x^10+264x^11+850x^12+540x^13+7902x^14+3336x^15+25866x^16+15804x^17+3332x^18+720x^19+330x^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 0.364 seconds.