The generator matrix

 1  0  1  1  1  4  1  1  0  1  1  0  1  1  2  1 14  1  1  6  1  1  1  2  1  1  1  0  1  0  2  1  4  1  2  2  4  2  1  2  1  8  2
 0  1  1  0 11  1  1  0  1 10 11  1 14  1  1  7  1  4 14  1 13 10  3  1 12  7  6  1  7  8  1  2  1  9  2 10  2  8 15  6 12  1  4
 0  0  2  0  0  8 10  2  2  2 12 14  0  8  2  6  4  2  0  8  4  6 14  6  2  6  4 14 10  2  0  2  0 12  2 10 10 10  6  2 12  0 12
 0  0  0  2  0 10 14 14  6  8  2 12 12  6  2  4  8  4  2  6  0 14 10  4  2  0 14  6  8  6  6 14  0  8 14  0 12 14 10  8  4 12 10
 0  0  0  0 12  0  0 12 12  4  4  4  8  4  4  8  8  4  0  8  0  8 12  8  0  4  4  0 12  8  0  8 12  4  0  4  0  4  0  0 12  4  4

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

Homogenous weight enumerator: w(x)=1x^0+234x^36+656x^37+1430x^38+2924x^39+5017x^40+7196x^41+9962x^42+10568x^43+10202x^44+7484x^45+4716x^46+2844x^47+1351x^48+500x^49+298x^50+80x^51+56x^52+4x^53+10x^54+3x^56

The gray image is a code over GF(2) with n=344, k=16 and d=144.
This code was found by Heurico 1.16 in 28.7 seconds.