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

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

Homogenous weight enumerator: w(x)=1x^0+40x^114+96x^117+92x^120+54x^121+86x^123+270x^124+98x^126+486x^127+4374x^128+70x^129+432x^130+48x^132+216x^133+46x^135+36x^138+32x^141+36x^144+16x^147+8x^150+16x^153+2x^156+4x^162+2x^177

The gray image is a code over GF(3) with n=576, k=8 and d=342.
This code was found by Heurico 1.16 in 0.445 seconds.