The generator matrix

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

generates a code of length 14 over Z27 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+72x^22+144x^23+44x^24+258x^25+1188x^26+90x^27+1764x^28+2376x^29+96x^30+270x^31+180x^32+4x^33+66x^34+2x^36+6x^39

The gray image is a code over GF(3) with n=126, k=8 and d=66.
This code was found by Heurico 1.16 in 0.0355 seconds.