The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+76x^35+219x^36+404x^37+950x^38+1330x^39+2454x^40+3294x^41+5053x^42+5166x^43+5204x^44+3360x^45+2401x^46+1222x^47+869x^48+408x^49+193x^50+70x^51+45x^52+20x^53+9x^54+8x^55+8x^56+2x^57+2x^58

The gray image is a code over GF(2) with n=344, k=15 and d=140.
This code was found by Heurico 1.16 in 11.4 seconds.