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  1  1  1  3  1  3  1  3  1
 0  3  0  0  0 24  9 18  0  9 18 12 15 15 12  3  6 12 21 24 12 15 24 15  6 12 24 12 21 15  0 18  3 18  3 24  9  6  6 15
 0  0  3  0  9 18 15 21  6 21  6  3 15 21  3  6  6 12 15  3  0  6 18  9 21  0  0 15 15 21  9  9 21  0 21  3  3 24 12  6
 0  0  0  3 15  0 18 15 12 12  6 24  9  9 18  0 21 21 24  6 15 24 24  3  3 12 12 12 21 12  3 15  9 18 18 15 15 24 21  9

generates a code of length 40 over Z27 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+696x^72+54x^74+1206x^75+324x^76+162x^77+3720x^78+1296x^79+2430x^80+5994x^81+1296x^82+270x^83+1236x^84+654x^87+300x^90+42x^93+2x^108

The gray image is a code over GF(3) with n=360, k=9 and d=216.
This code was found by Heurico 1.16 in 2.02 seconds.