The generator matrix

 1  0  1  1  1  6  1  0  1  1 14  1  1  8  1  2  1  1
 0  1 11  6 13  1  6  1  3  8  1 11  5  1 13  8 14  5
 0  0 12  0  4  4  8  4 12  4  0  0  8 12  8  8  8  0
 0  0  0 12  0  4  8 12 12  0 12 12  0  8 12 12 12  8
 0  0  0  0  8  0  8  8  0  0  8  8  0  0  8  0  8  8
 0  0  0  0  0  8  0  8  0  8  8  0  8  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+76x^13+160x^14+558x^15+1524x^16+3462x^17+4835x^18+3452x^19+1523x^20+584x^21+123x^22+54x^23+23x^24+6x^25+1x^26+1x^28+1x^30

The gray image is a code over GF(2) with n=144, k=14 and d=52.
This code was found by Heurico 1.16 in 11.3 seconds.