The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+178x^14+328x^15+682x^16+1328x^17+3132x^18+1376x^19+720x^20+272x^21+130x^22+24x^23+20x^24+1x^32

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 0.262 seconds.