The generator matrix

 1  0  1  1  1 21  1  1  0  1  1  9  1  1  3 24
 0  1  7 21  4  1  0 16  1  9 16  1 24 19 24  1
 0  0  9 18  0 18  9 18  9 18  0 18  0  9  9  9

generates a code of length 16 over Z27 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+234x^29+516x^30+180x^32+1014x^33+234x^35+6x^36+2x^45

The gray image is a code over GF(3) with n=144, k=7 and d=87.
This code was found by Heurico 1.16 in 53 seconds.