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

generates a code of length 66 over Z27 who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+64x^114+158x^117+242x^120+18x^122+202x^123+180x^125+220x^126+720x^128+176x^129+1440x^131+13322x^132+1440x^134+160x^135+576x^137+182x^138+142x^141+124x^144+132x^147+84x^150+56x^153+22x^156+8x^159+10x^162+2x^168+2x^183

The gray image is a code over GF(3) with n=594, k=9 and d=342.
This code was found by Heurico 1.16 in 3.43 seconds.