The generator matrix

 1  0  1  1  1  1  1 18  1 24  1  1  1  0
 0  1  1 26  0 25 17  1 18  1  4 24 22  1
 0  0 24  0  9  3 21  3 21  6 18 21  3 21
 0  0  0  3 15  9 15 15  9  0  6 12 24 21

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

Homogenous weight enumerator: w(x)=1x^0+546x^22+360x^23+1522x^24+1656x^25+8316x^26+5052x^27+16596x^28+16632x^29+5178x^30+2424x^31+450x^32+144x^33+162x^34+8x^36+2x^42

The gray image is a code over GF(3) with n=126, k=10 and d=66.
This code was found by Heurico 1.16 in 2.72 seconds.