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

generates a code of length 71 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+58x^123+158x^126+156x^129+254x^132+54x^134+182x^135+432x^137+232x^138+1296x^140+174x^141+13122x^142+1728x^143+176x^144+864x^146+128x^147+162x^150+148x^153+124x^156+78x^159+54x^162+54x^165+26x^168+10x^171+6x^174+4x^177+2x^201

The gray image is a code over GF(3) with n=639, k=9 and d=369.
This code was found by Heurico 1.16 in 3.76 seconds.