The generator matrix

 1  1  1  1  1  1  1  3  1  3  0  1  1  1
 0  3 24  0 21 24  0 21 21 24  3  9 24  0
 0  0  9  0  0  0  9 18 18 18  9 18  0  9
 0  0  0  9  0  9  9  9  9 18  9  0  0 18
 0  0  0  0 18 18  9  9 18  0  9 18 18  0

generates a code of length 14 over Z27 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+58x^21+54x^22+138x^24+324x^25+1458x^26+188x^27+648x^28+2916x^29+220x^30+432x^31+96x^33+18x^36+10x^39

The gray image is a code over GF(3) with n=126, k=8 and d=63.
This code was found by Heurico 1.16 in 0.218 seconds.