The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+330x^22+360x^23+388x^24+360x^25+540x^26+516x^27+14004x^28+1080x^29+642x^30+696x^31+450x^32+144x^33+162x^34+8x^36+2x^42

The gray image is a code over GF(3) with n=126, k=9 and d=66.
This code was found by Heurico 1.16 in 1.45 seconds.