The generator matrix

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

generates a code of length 72 over Z27 who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+32x^138+54x^141+2028x^144+38x^147+18x^150+12x^153+2x^156+2x^216

The gray image is a code over GF(3) with n=648, k=7 and d=414.
This code was found by Heurico 1.16 in 0.179 seconds.