The generator matrix

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

generates a code of length 44 over Z27 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+68x^72+192x^75+204x^78+426x^81+956x^84+1698x^87+13122x^88+1650x^90+784x^93+198x^96+168x^99+112x^102+54x^105+34x^108+8x^111+6x^114+2x^117

The gray image is a code over GF(3) with n=396, k=9 and d=216.
This code was found by Heurico 1.16 in 2.01 seconds.