The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+912x^34+1242x^35+4590x^36+9192x^37+21522x^38+23586x^39+65364x^40+70824x^41+89682x^42+119364x^43+72414x^44+32366x^45+16008x^46+4002x^47+166x^48+84x^49+96x^50+24x^51+2x^57

The gray image is a code over GF(3) with n=189, k=12 and d=102.
This code was found by Heurico 1.16 in 129 seconds.