The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  2  1
 0 12  0  0  8 12 12  4  0  0  8 12  0  4  8 12 12  4
 0  0 12  0 12 12  4  8  0  4  4 12  8 12  0  4 12  0
 0  0  0 12  4  8  4  4  8  4  0  0  4  8  0  4  4  4

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

Homogenous weight enumerator: w(x)=1x^0+21x^14+46x^15+46x^16+80x^17+637x^18+92x^19+42x^20+32x^21+12x^22+6x^23+7x^24+1x^26+1x^30

The gray image is a code over GF(2) with n=144, k=10 and d=56.
This code was found by Heurico 1.16 in 0.00719 seconds.