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

generates a code of length 44 over Z27 who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+54x^88+20x^90+2x^93+2x^96+2x^99

The gray image is a code over GF(3) with n=396, k=4 and d=264.
This code was found by Heurico 1.16 in 0.0197 seconds.