The generator matrix

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

generates a code of length 24 over Z27 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+66x^40+142x^42+168x^43+132x^45+798x^46+3096x^48+1602x^49+180x^51+210x^52+68x^54+66x^55+6x^58+18x^60+6x^63+2x^69

The gray image is a code over GF(3) with n=216, k=8 and d=120.
This code was found by Heurico 1.16 in 0.0802 seconds.