The generator matrix

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

generates a code of length 22 over Z27 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+1074x^36+1650x^37+4692x^38+10096x^39+21348x^40+23808x^41+67218x^42+70206x^43+83520x^44+120490x^45+71718x^46+32442x^47+17934x^48+4608x^49+348x^50+180x^51+84x^52+18x^53+4x^54+2x^57

The gray image is a code over GF(3) with n=198, k=12 and d=108.
This code was found by Heurico 1.16 in 138 seconds.