The generator matrix

 1  0  0  1  1 15  1  1  1  1  1  1  0  1 24  1 24  1  1  1  1  1  1 24  1  9  1  1  1  1 18  6 12  1  1  1  1  1
 0  1  0  0 21  1 25  1 17  2 16 14  1 18 24 22  1 19 23 12 10 14 20  1 22  1 26 20 12 20  1  1  1  1 16 24 21 12
 0  0  1  7 14 16  2  1 21  2 15 16 26 21  1 20  9 24  0 10 13 23  1 13  3  2 23 13  4 16 17 19 25  7 22  9 25  7
 0  0  0  9 18  0  9  9  0  0 18 18 18 18 18 18  9  9  9  0  0  9  0 18  0  9 18  9 18  9  0  0 18  0 18 18  0 18

generates a code of length 38 over Z27 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+690x^69+1152x^70+2040x^71+4222x^72+3600x^73+5436x^74+8130x^75+6270x^76+8478x^77+8572x^78+4164x^79+2820x^80+2288x^81+828x^82+162x^83+120x^84+12x^85+18x^86+32x^87+12x^88+2x^90

The gray image is a code over GF(3) with n=342, k=10 and d=207.
This code was found by Heurico 1.16 in 4.14 seconds.