The generator matrix

 1  0  0  1  1  1 15  1  1  3  1  1  1 21  1  1  1  1  0  9  1
 0  1  0  1 15 26  1 19 20  1 18 17 16  1 18 20 25 21  1 24 18
 0  0  1 26 16 26 22 19 21 23 20 19 15  9 22 12 15  2 23  1 21
 0  0  0 24 15  9  3 21  3 12  6 15 18 24 21  6 12  9  6 24 24

generates a code of length 21 over Z27 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+174x^34+342x^35+2100x^36+2898x^37+5664x^38+11174x^39+19266x^40+20820x^41+37036x^42+36420x^43+21042x^44+14762x^45+4320x^46+690x^47+260x^48+102x^49+42x^50+32x^51+2x^57

The gray image is a code over GF(3) with n=189, k=11 and d=102.
This code was found by Heurico 1.16 in 15.8 seconds.