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  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 18  9  9 18  0 18 18  0  9  0  9 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  0  9  9  0  9  0  0 18 18  9 18 18  0
 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 18  0 18  9  9 18  9  0  0  0  9  9 18

generates a code of length 70 over Z27 who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+114x^137+188x^138+360x^141+4x^144+42x^146+8x^147+4x^153+6x^155+2x^156

The gray image is a code over GF(3) with n=630, k=6 and d=411.
This code was found by Heurico 1.16 in 4.23 seconds.