The generator matrix

 1  0  0  0  1  1  1
 0  1  0  0 15 25  1
 0  0  1  0 16 23  1
 0  0  0  1 14  2 24

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

Homogenous weight enumerator: w(x)=1x^0+696x^8+156x^9+8208x^10+4176x^11+68494x^12+32832x^13+241308x^14+136974x^15+32832x^16+5568x^17+188x^18+8x^21

The gray image is a code over GF(3) with n=63, k=12 and d=24.
This code was found by Heurico 1.16 in 11.6 seconds.