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

generates a code of length 71 over Z27 who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+114x^139+162x^140+44x^141+324x^143+22x^144+42x^148+8x^150+4x^153+6x^157+2x^159

The gray image is a code over GF(3) with n=639, k=6 and d=417.
This code was found by Heurico 1.16 in 5.09 seconds.