The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+120x^8+34x^9+972x^10+720x^11+5898x^12+3888x^13+30762x^14+11754x^15+3888x^16+960x^17+46x^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 0.181 seconds.