The generator matrix

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

generates a code of length 13 over Z27 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+84x^22+36x^23+132x^24+108x^25+1548x^26+56x^27+72x^28+36x^29+52x^30+60x^31+2x^39

The gray image is a code over GF(3) with n=117, k=7 and d=66.
This code was found by Heurico 1.16 in 0.00428 seconds.