The generator matrix

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

generates a code of length 38 over Z27 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+126x^67+228x^68+398x^69+372x^70+390x^71+1010x^72+912x^73+1722x^74+2504x^75+3408x^76+3234x^77+2510x^78+1080x^79+492x^80+310x^81+324x^82+186x^83+220x^84+84x^85+48x^86+86x^87+6x^88+18x^89+6x^90+6x^91+2x^99

The gray image is a code over GF(3) with n=342, k=9 and d=201.
This code was found by Heurico 1.16 in 1.05 seconds.