The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  6  1  1  1 12  1  1 12 10  1  1  1  1  6  1  1  1  0  6  0  1 12  1 10  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  6  1  5 15 12  1  9 10  1  1  6  0 10  3  1 15  5 15  1  1  1 12  1  3  1  6  5  5
 0  0  8  0  0  0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  8  8  0  8  0  8  8  0  0  8  0  0  8  8  0  0  8  8  8  8  8  8  8
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  8  8  0  8  8  0  8  8  8  0  0  8  0  8  0  8  8  8  8  0  8  8  8
 0  0  0  0  8  0  0  0  0  8  8  0  0  8  0  8  8  8  0  0  8  8  8  8  0  0  0  0  8  0  8  8  0  0  8  0  8  8  8  8  8  8  8
 0  0  0  0  0  8  0  0  8  8  0  0  0  8  8  8  8  0  8  0  0  8  0  8  0  8  8  8  0  0  0  0  8  0  8  8  8  8  8  0  0  0  8
 0  0  0  0  0  0  8  0  8  0  0  8  8  8  0  8  8  0  8  8  0  0  8  8  0  0  0  8  0  0  8  8  8  8  0  8  0  0  0  0  8  8  8
 0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  0  0  8  0  8  8  8  0  0  8  0  8  0  8  8  0  8  0  0  0  8  8  0  0  0  8  0

generates a code of length 43 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+97x^36+40x^37+220x^38+560x^39+1135x^40+2136x^41+2388x^42+3232x^43+2443x^44+2136x^45+1060x^46+560x^47+259x^48+40x^49+44x^50+15x^52+13x^56+5x^60

The gray image is a code over GF(2) with n=344, k=14 and d=144.
This code was found by Heurico 1.16 in 2.17 seconds.