The generator matrix

 1  1  1  1  1  1  1  1  1  3  1  1  1  1
 0  9  0  0  9  0  9  9 18  9  0  0  9  9
 0  0  9  0 18  9 18  9 18  0  0  9  9 18
 0  0  0  9 18 18  0 18 18  9 18  9  0 18

generates a code of length 14 over Z27 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+30x^24+54x^26+20x^27+486x^28+108x^29+12x^30+6x^33+6x^36+6x^39

The gray image is a code over GF(3) with n=126, k=6 and d=72.
This code was found by Heurico 1.16 in 0.00128 seconds.