The generator matrix

 1  0  1  1  1  1  1  0  1  1  1 15  1  1  1 24  1  3  1 12  1  1  1 21  1  1  1 12  1  1  1  1  3  6 12  1  1 18  1
 0  1  1 26 18 25 17  1  0 22 26  1  3 19 20  1  4  1  5  1 22  0 17  1  8  2  1  1 13 19  0  3  3  1  1  2  2  1 21
 0  0 24  0 18  0 21 24 18 21 15 12  3 24 18  0  9 21  0 15 15 15  3 15 15  6 21  9 18 15  3 24 24  9  0  6  9 12  6
 0  0  0  3 21 12 18  9 24  6 15  0 18 15 15  6 24 15  9  3  3  0 15 24 18 12  9  3  0 12 21 21 24 24  9 24  0  6 24

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

Homogenous weight enumerator: w(x)=1x^0+278x^69+246x^70+744x^71+1460x^72+1416x^73+3306x^74+4348x^75+4554x^76+7836x^77+8250x^78+7332x^79+8088x^80+5828x^81+2256x^82+1734x^83+710x^84+192x^85+120x^86+184x^87+36x^88+42x^89+82x^90+6x^94

The gray image is a code over GF(3) with n=351, k=10 and d=207.
This code was found by Heurico 1.16 in 5.22 seconds.