The generator matrix
1 1 1 1 1 1 1 1 1 3 3 1
0 3 24 9 21 6 18 12 15 21 24 0
generates a code of length 12 over Z27 who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+42x^22+12x^23+92x^24+84x^25+6x^26+4x^27+2x^30
The gray image is a code over GF(3) with n=108, k=5 and d=66.
This code was found by Heurico 1.16 in 0.000391 seconds.