The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1
 0  9  0  0  9  0  9  9 18  0  0  9  9  0 18  9 18 18  9  0
 0  0  9  0 18  9 18  9 18  0  9  9  0 18  0  0  9  9  9  0
 0  0  0  9 18 18  0 18 18 18  9  0 18  0 18  9  9  0  9  0

generates a code of length 20 over Z27 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+22x^36+54x^38+38x^39+486x^40+108x^41+4x^45+14x^48+2x^57

The gray image is a code over GF(3) with n=180, k=6 and d=108.
This code was found by Heurico 1.16 in 0.00259 seconds.