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

generates a code of length 68 over Z27 who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+34x^117+148x^120+212x^123+230x^126+90x^127+190x^129+360x^130+194x^132+900x^133+200x^135+14652x^136+200x^138+1098x^139+154x^141+396x^142+130x^144+122x^147+96x^150+110x^153+92x^156+40x^159+22x^162+4x^165+4x^168+2x^171+2x^186

The gray image is a code over GF(3) with n=612, k=9 and d=351.
This code was found by Heurico 1.16 in 3.54 seconds.