The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^36+324x^37+497x^38+1350x^39+2024x^40+4054x^41+5160x^42+6012x^43+4932x^44+4020x^45+2178x^46+1304x^47+373x^48+296x^49+84x^50+36x^51+16x^52+8x^53+13x^54+2x^55+2x^56+2x^57+4x^58

The gray image is a code over GF(2) with n=344, k=15 and d=144.
This code was found by Heurico 1.16 in 7.59 seconds.