The generator matrix

 1  0  0  0  1  1  1  1
 0  1  0  0 15 19 22 14
 0  0  1  0 16 19 14 21
 0  0  0  1 14 21 16 22

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

Homogenous weight enumerator: w(x)=1x^0+1104x^10+240x^11+9164x^12+6624x^13+70776x^14+36608x^15+219636x^16+141552x^17+36584x^18+8832x^19+300x^20+16x^21+4x^24

The gray image is a code over GF(3) with n=72, k=12 and d=30.
This code was found by Heurico 1.16 in 20.1 seconds.