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

generates a code of length 62 over Z27 who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+242x^120+476x^123+972x^124+384x^126+64x^129+46x^132+2x^180

The gray image is a code over GF(3) with n=558, k=7 and d=360.
This code was found by Heurico 1.16 in 0.132 seconds.