The generator matrix

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

generates a code of length 16 over Z27 who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+72x^25+384x^26+378x^27+240x^28+414x^29+570x^30+414x^31+14220x^32+736x^33+594x^34+858x^35+404x^36+138x^37+162x^38+94x^39+2x^42+2x^48

The gray image is a code over GF(3) with n=144, k=9 and d=75.
This code was found by Heurico 1.16 in 23.9 seconds.