The generator matrix

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

generates a code of length 14 over Z27 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+48x^20+104x^21+108x^22+318x^23+360x^24+288x^25+3756x^26+710x^27+4968x^28+6918x^29+752x^30+432x^31+600x^32+234x^33+36x^34+24x^35+18x^36+8x^39

The gray image is a code over GF(3) with n=126, k=9 and d=60.
This code was found by Heurico 1.16 in 0.265 seconds.