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

generates a code of length 69 over Z27 who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+52x^120+188x^123+216x^126+224x^129+54x^130+220x^132+432x^133+202x^135+1296x^136+13316x^138+1728x^139+142x^141+864x^142+152x^144+128x^147+146x^150+110x^153+88x^156+54x^159+48x^162+16x^165+4x^168+2x^195

The gray image is a code over GF(3) with n=621, k=9 and d=360.
This code was found by Heurico 1.16 in 3.63 seconds.