The generator matrix

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

generates a code of length 39 over Z27 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+216x^69+210x^70+204x^71+610x^72+360x^73+942x^74+996x^75+2100x^76+2898x^77+1450x^78+3918x^79+2880x^80+1142x^81+474x^82+210x^83+430x^84+150x^85+144x^86+182x^87+66x^88+12x^89+52x^90+12x^91+14x^93+6x^96+4x^99

The gray image is a code over GF(3) with n=351, k=9 and d=207.
This code was found by Heurico 1.16 in 1.16 seconds.