The generator matrix

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

generates a code of length 24 over Z27 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+162x^44+96x^45+216x^46+234x^47+716x^48+432x^49+162x^50+54x^51+54x^53+20x^54+36x^56+2x^57+2x^66

The gray image is a code over GF(3) with n=216, k=7 and d=132.
This code was found by Heurico 1.16 in 0.0109 seconds.