The generator matrix

 1  0  0  1  1  1  2 10  1  1  1  1 14  6  2  8  1  1  1  4 12  1  1  1 10  1  8 14  1  1  1 12 12  1  0  6  6  1  0  1  1  8  1  1
 0  1  0  0 13  5  1  2  5  9 10  2  1  1  1  6 15  8  7  1  1 14  7  3  1 11  1  1  2 12  0  6  1  2  1  1 12  1 12  0 13 10  8  0
 0  0  1 11  3  0  3  1  5  2  4  7  6  5  4  1  9 14 12  9  3  9 10  7  4 13  7  6 14 11 12  1  1  0  6 10  1  8  1 13  5  1  5  8
 0  0  0 12  4  8  4 12  0 12  4  8 12  0  0  4  4  8  8  8 12  0 12  4 12  0  8  8  4  8  4  0  4  0  0  4  0  4  4 12  4 12  0  8

generates a code of length 44 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+176x^39+853x^40+1252x^41+2281x^42+2330x^43+3062x^44+2030x^45+2189x^46+1056x^47+700x^48+272x^49+111x^50+38x^51+14x^52+12x^53+3x^54+2x^60+2x^61

The gray image is a code over GF(2) with n=352, k=14 and d=156.
This code was found by Heurico 1.16 in 1.75 seconds.