The generator matrix

 1  0  0  0  1  1  1  1  8  1  1  1  4  8 14  6  1  1  1  2  1  1 14  6  1  1  0 10  2  1  4  1  1  1  1  1  6  8  1  0  1 14  1
 0  1  0  0  0  8  5 15  1 11 13  4 10  1  1  8 10  2  3  1  7 12  4  1  7  2  1  1  1  0 12  7  2  5  6  2  1  1  9  6 12  0  0
 0  0  1  0  1 14  4  2  2  3 13  7  1 11  7  1  1  6  9  4  4 13  1 12 10 12 12  2 15 13 10  1 11  3  4 12 13 13  8  1  8 14  0
 0  0  0  1  1  3  7 10  3  9  2  8 13  1  8 14 12 15 13 14  4  7  7  1  9 10 13  8  6  4  1  3  9 10  8  1 11  1  3 15  5  1  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  0  8  0  8  8  0  0  0  8  0  8  8  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+130x^36+1050x^37+2489x^38+5820x^39+9265x^40+16034x^41+19130x^42+22508x^43+19903x^44+16810x^45+9011x^46+5294x^47+2245x^48+958x^49+244x^50+120x^51+33x^52+12x^53+6x^54+2x^55+7x^56

The gray image is a code over GF(2) with n=344, k=17 and d=144.
This code was found by Heurico 1.16 in 91.1 seconds.