The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  4  1  2  2  1  1  0  2  1  1  1  1  1  2  8  2  1  1  0  2  2  2  0  1
 0  2  0  6  4  6 12  2  6 14  8 12  0  4  2 10 14  2 14  2  0  6 10  2  4  2  6  8  6  6  0 10  2  2  2 14  4  8 14 14 10  8 14
 0  0 12  0  4  0  0  8  4 12  0  4  4  8 12 12  8  0  0  8 12  0  8 12  0  4  4  4  0  4  8  4  4  4  8  8  4  4 12 12  4  4 12
 0  0  0 12  0  0  0 12  4  8 12 12  4 12  8 12  4  4  8 12  8  0  0  8 12  4  4  8  8 12  8  0  8  8  4  4  4  0  8  0  8 12  4
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  0  8  8  0  8  0  0  8  8  8  0  8  8  8  0  0  0  8  8  8
 0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  8  0  8  8  0  0  8  0  0  8  8  8
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  8  0  8  8  0  8  8  8  8  0  8  0  0  0  0  8  8  8  0  0  0  8  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+204x^36+116x^37+558x^38+544x^39+1745x^40+1196x^41+3170x^42+1320x^43+3184x^44+1388x^45+1650x^46+432x^47+489x^48+116x^49+174x^50+8x^51+66x^52+16x^54+5x^56+2x^60

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 5.38 seconds.