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

generates a code of length 72 over Z27 who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+58x^126+174x^129+6x^130+246x^132+12x^133+236x^135+180x^136+210x^138+600x^139+174x^141+1020x^142+13270x^144+1440x^145+176x^147+852x^148+200x^150+264x^151+132x^153+110x^156+100x^159+82x^162+64x^165+32x^168+18x^171+20x^174+2x^177+2x^183+2x^195

The gray image is a code over GF(3) with n=648, k=9 and d=378.
This code was found by Heurico 1.16 in 3.85 seconds.