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

generates a code of length 44 over Z27 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+228x^84+54x^85+252x^86+298x^87+540x^88+378x^89+276x^90+54x^91+30x^93+18x^95+30x^96+26x^99+2x^123

The gray image is a code over GF(3) with n=396, k=7 and d=252.
This code was found by Heurico 1.16 in 3.3 seconds.