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  3  1  1  1  3  1  1  0  1  3  1  1  1  1  1  1  3  1  1  0  1  0  1  1  3  1  1
 0  3 24  0 21 24  0 21 24  9 21 24  6  0 21 12  6  9 24  0 21 12  0 24  6  3  0  6 21 18 12 15  9 24 12  3  9 21 15 18 12 24 15  3  3 21 21 15  6 24 18  9  6 24  9  6  3  9  3 24  6 21  0  0
 0  0  9  0  0  0  0 18  9  0  9 18 18  0  0  9  0  0  9 18 18  9  9 18  9  9  9  9  9 18  9  0  9  9 18  0  0 18  0 18 18  0 18  9  0 18 18  0 18 18  9  9 18  0  0  9  0  0  0 18  0  9  9  0
 0  0  0  9  0  0  0  0  0 18  0  9 18  9  9  9  9 18  9 18  9  9  0 18 18  0  9 18  9 18 18  9 18 18  9  9 18  0 18 18 18  9  9 18 18  9  9  9  9  9  0  0  9  9  0  0 18  9  9 18 18  9  9  0
 0  0  0  0 18  0  9 18  9  9  0  9 18  0 18  0 18  0 18 18  0  0 18  9  0  0 18 18 18 18 18  0  9 18 18  9  9  9 18  0 18 18 18  9 18  0  0  9  0 18  0  0  9  9 18 18  0  0  9 18  0 18  9  0
 0  0  0  0  0  9  9  0 18  9  0  0  9  9 18 18  9  9  0 18  0  0 18  9 18  9  9  9  9  9 18  9  9  0 18  0  0 18  9  9 18 18  9  0 18  9 18  0  9  0 18  0  9  0 18  0  0 18 18 18  0  9 18  0

generates a code of length 64 over Z27 who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+44x^114+72x^116+226x^117+24x^118+168x^119+508x^120+102x^121+468x^122+422x^123+732x^124+2142x^125+622x^126+2376x^127+4164x^128+496x^129+2328x^130+2808x^131+524x^132+186x^133+162x^134+388x^135+84x^136+150x^137+234x^138+72x^140+90x^141+36x^144+20x^147+14x^150+12x^153+2x^156+2x^159+2x^162+2x^168

The gray image is a code over GF(3) with n=576, k=9 and d=342.
This code was found by Heurico 1.16 in 2.33 seconds.