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

generates a code of length 70 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+116x^123+6x^125+206x^126+36x^128+214x^129+138x^131+236x^132+438x^134+194x^135+918x^137+184x^138+14322x^140+208x^141+1014x^143+146x^144+504x^146+116x^147+120x^149+138x^150+126x^153+110x^156+96x^159+50x^162+22x^165+16x^168+6x^171+2x^183

The gray image is a code over GF(3) with n=630, k=9 and d=369.
This code was found by Heurico 1.16 in 4.68 seconds.