The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+89x^36+88x^37+140x^38+272x^39+635x^40+1064x^41+932x^42+1760x^43+979x^44+1064x^45+564x^46+272x^47+179x^48+88x^49+28x^50+15x^52+17x^56+5x^60

The gray image is a code over GF(2) with n=344, k=13 and d=144.
This code was found by Heurico 1.16 in 0.979 seconds.