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

generates a code of length 69 over Z27 who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+102x^126+6x^127+86x^129+66x^130+118x^132+192x^133+92x^135+342x^136+4442x^138+474x^139+52x^141+294x^142+54x^144+84x^145+26x^147+30x^150+32x^153+26x^156+12x^159+14x^162+8x^165+2x^168+2x^171+2x^174+2x^186

The gray image is a code over GF(3) with n=621, k=8 and d=378.
This code was found by Heurico 1.16 in 0.585 seconds.