The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  3  3  1  1
 0  3 24  0 21 24  9 21  6  9 12  6  9 21 12 24 24  9  0  3
 0  0  9  9 18 18 18  9  0  9  0  9  0  9  9  0  9 18 18 18

generates a code of length 20 over Z27 who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+36x^37+168x^38+12x^39+204x^40+252x^41+10x^42+24x^43+2x^45+6x^46+12x^47+2x^51

The gray image is a code over GF(3) with n=180, k=6 and d=111.
This code was found by Heurico 1.16 in 0.0117 seconds.