The generator matrix

 1  0  1  1  1  6  1 12  1  1 14  1  1  8  1  1 14  1
 0  1 11  6 13  1 12  1  3  5  1 14  8  1  9  4  1  3
 0  0 12  0  4  0  0  8  0  8  4 12 12  4  8 12 12  8
 0  0  0  8  0  0  8  0  0  0  8  8  8  0  8  0  0  8
 0  0  0  0  8  0  8  8  8  8  8  0  8  8  0  8  0  8
 0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  0  0  8

generates a code of length 18 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+104x^14+192x^15+945x^16+1600x^17+2532x^18+1600x^19+920x^20+192x^21+80x^22+22x^24+4x^26

The gray image is a code over GF(2) with n=144, k=13 and d=56.
This code was found by Heurico 1.16 in 0.988 seconds.