The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  9  1  1  1  1  1 15  1  6  1  1 21  1  6 18  1  1  3  1  1  1 21  1  1  1  1  0  1 21  1  1
 0  1  0 18 21 16 25 20 11  4 26  1  9 19 10  3  2  1 14  1 23 15  1 16 18  1 22  1  1 24  8 11 21 12 26  5  6  1 17  1 13  0
 0  0  1 16 14  5 25  9  4  6  8 17  3  1  2 11 24 14 13 25 17 25 13 26  1 15 26  4  0 12  3 16  1 13 24  5 14  7  5 26  2 18

generates a code of length 42 over Z27 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+336x^78+414x^79+2322x^80+1560x^81+1338x^82+3570x^83+1918x^84+1314x^85+2934x^86+1336x^87+774x^88+1362x^89+404x^90+48x^91+12x^92+26x^93+2x^96+6x^98+6x^99

The gray image is a code over GF(3) with n=378, k=9 and d=234.
This code was found by Heurico 1.16 in 0.516 seconds.