The generator matrix

 1  0  1  1  1  4  1  1  2 14  1  1  1  1 10  1 10  1
 0  1  1  0  3  1  2  5  1  1 14 11  7  9  1 10  1  2
 0  0  2  6  0  2  2  4  6  8  0  4  6  2  2 14 14 12
 0  0  0 12  0  8  8 12  4  4  4  0  4  4 12  8  0  8
 0  0  0  0  8  8  0  8  8  0  0  0  8  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+234x^14+468x^15+1632x^16+3512x^17+4707x^18+3488x^19+1672x^20+456x^21+176x^22+12x^23+21x^24+3x^26+2x^28

The gray image is a code over GF(2) with n=144, k=14 and d=56.
This code was found by Heurico 1.16 in 18.3 seconds.