The generator matrix

 1  0  0  1  1  1  1  1  1  3  1 15  1  1  1  3  1  9  1  1  0  1  1  6  1  0 15  1  1  1  1  1  1  1  1  1  1 15
 0  1  0  1 18  1  2  0 25  1 17  1 20 19  8  6  5  1  5 12  1  3 15  1  4  1  1 12  6 26 25 23 14  9  9 16  5  1
 0  0  1 26 16  1 13 26  3  2 18 16 14 22 15  1 11 15 25 26 19 16 12 12  5  7 20  1  2  4  8 14 15  3 12 13  9 21
 0  0  0 24 18 15 21  6  9  0  3 15  0  9  6 21  6 15  9  0 21 24  6 12 21  9  3  3 12 15 18 12  0  3 24 24 18  0

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

Homogenous weight enumerator: w(x)=1x^0+426x^67+834x^68+1784x^69+4554x^70+5730x^71+8266x^72+12174x^73+15582x^74+22858x^75+23106x^76+25032x^77+23274x^78+16716x^79+8916x^80+4234x^81+2586x^82+636x^83+74x^84+192x^85+126x^86+16x^87+24x^88+6x^89

The gray image is a code over GF(3) with n=342, k=11 and d=201.
This code was found by Heurico 1.16 in 34.5 seconds.