The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  1  1
 0  1 16 26 21  4 20  1 24 19 23  1  9 12

generates a code of length 14 over Z27 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+180x^26+86x^27+54x^28+360x^29+42x^30+6x^33

The gray image is a code over GF(3) with n=126, k=6 and d=78.
This code was found by Heurico 1.16 in 0.000651 seconds.