The generator matrix

 1  0  0  1  1 15  9  1  1  1  1  1  1  1 21  1  1  0  1  1 12  1  1  1 24 15  1  1  1  1 24  1 18 12  3  1  1 12  1
 0  1  0  0 21  1  1 16  1 14 26 17 16 14  1 19 24  1  5 15 18  3 23 13 24  1 13  9 23 26  1 12  1  1  1 21 19  1 25
 0  0  1  7 14 16 17 17  1 16 24 20 15 11 15 14 17 22  1 10  1 18  6  7  1 13 19 21  9 26 17 19 24  9 14 18 12 10 21
 0  0  0  9 18  0  0 18 18 18  0  9  9  0 18  0  9 18  9 18  9  9  9  0 18  9  9  9  0 18  0  0 18  9  9  0  0 18 18

generates a code of length 39 over Z27 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+834x^71+1224x^72+1818x^73+4332x^74+4108x^75+5004x^76+7350x^77+7242x^78+7884x^79+8082x^80+4784x^81+2772x^82+2556x^83+820x^84+18x^85+120x^86+30x^87+48x^89+12x^90+6x^92+4x^93

The gray image is a code over GF(3) with n=351, k=10 and d=213.
This code was found by Heurico 1.16 in 78.6 seconds.