The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+43x^36+138x^37+341x^38+634x^39+1290x^40+1850x^41+2445x^42+2964x^43+2505x^44+1876x^45+1141x^46+580x^47+325x^48+114x^49+65x^50+28x^51+26x^52+6x^53+7x^54+2x^55+2x^56+1x^62

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 2.08 seconds.