The generator matrix

 1  0  1  1  1  1  1 21  1  1 24  1  1  1  1  1  0  1  1 21  1  1  0  1  1  1  1 21  1  1 21  1  1  1 12  1  1  1  1
 0  1  7 26 21  4 20  1 19 24  1 23 26 16  0  4  1 21 20  1 19 24  1 26 21 24 20  1 19  4  1  0 26 16  1  0  9 21  0
 0  0  9  0  0  0 18  9 18  9  9  9  9  0 18  0  0  9 18  0 18  9  0  9 18  9  0 18  0  9  9  9 18  0  9  0  9 18  9
 0  0  0  9  0  9  9  9 18 18  0 18  0  9  9  0  9  0  9 18  0  0 18 18 18  0 18  0 18  0 18 18 18  0 18 18 18  0  9
 0  0  0  0 18 18  0 18 18  9 18 18  9  9  9  9  0  0 18  9  9  9 18  0  9 18  9 18 18 18 18  9  9  9  0 18 18  0  0

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

Homogenous weight enumerator: w(x)=1x^0+62x^69+84x^70+138x^71+618x^72+372x^73+300x^74+2606x^75+1938x^76+588x^77+4576x^78+3192x^79+618x^80+3190x^81+654x^82+294x^83+318x^84+60x^85+6x^86+16x^87+18x^88+14x^90+6x^93+8x^96+2x^99+4x^102

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 0.624 seconds.