The generator matrix

 1  0  1  1  1  1  1
 0  1  1 26  0 16  0
 0  0 24  0  3 15 18
 0  0  0  3  3  6  6

generates a code of length 7 over Z27 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+108x^8+130x^9+648x^10+648x^11+7446x^12+2592x^13+28998x^14+14850x^15+2592x^16+864x^17+166x^18+6x^21

The gray image is a code over GF(3) with n=63, k=10 and d=24.
This code was found by Heurico 1.16 in 0.218 seconds.