The generator matrix

 1  0  0  1  1  1  1  1  1 15  1  1  1  1
 0  1  0 15  1 16 17  9 20  1  7  5  6  3
 0  0  1 16  1 15 20 17  6 16 14 25 21 10

generates a code of length 14 over Z27 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+48x^23+854x^24+954x^25+1824x^26+2906x^27+5388x^28+3552x^29+3090x^30+942x^31+84x^32+34x^33+6x^34

The gray image is a code over GF(3) with n=126, k=9 and d=69.
This code was found by Heurico 1.16 in 0.131 seconds.