The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+56x^37+280x^38+410x^39+998x^40+1024x^41+2189x^42+1882x^43+2842x^44+1818x^45+2200x^46+1060x^47+899x^48+280x^49+250x^50+90x^51+54x^52+18x^53+8x^54+14x^55+6x^56+4x^57+1x^58

The gray image is a code over GF(2) with n=352, k=14 and d=148.
This code was found by Heurico 1.16 in 3.2 seconds.