The generator matrix

 1  1  1  1  1  1  1  1  1  2  1  2  8  1  2  2  1  1
 0  2  0  2  0 10  8  6  4  0  0 12  4 14  2  6  4  8
 0  0  2  2 12 14 14  0  4  6  6 10  2  4  2  0  2  4
 0  0  0  8  0  0  0  8  8  0  8  0  8  0  8  0  0  8
 0  0  0  0  8  0  8  0  0  8  8  0  8  0  0  8  0  8
 0  0  0  0  0  8  0  8  8  8  8  0  0  8  8  0  8  0

generates a code of length 18 over Z16 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+40x^13+153x^14+374x^15+627x^16+2024x^17+1770x^18+2014x^19+636x^20+368x^21+122x^22+42x^23+16x^24+2x^26+2x^27+1x^30

The gray image is a code over GF(2) with n=144, k=13 and d=52.
This code was found by Heurico 1.16 in 0.195 seconds.