The generator matrix

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

generates a code of length 20 over Z27 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+888x^32+774x^33+4752x^34+8214x^35+18808x^36+26568x^37+67200x^38+61946x^39+100278x^40+125310x^41+63288x^42+36072x^43+13980x^44+3106x^45+192x^47+62x^48+2x^57

The gray image is a code over GF(3) with n=180, k=12 and d=96.
This code was found by Heurico 1.16 in 120 seconds.