The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+92x^37+262x^38+616x^39+1364x^40+2682x^41+3142x^42+5728x^43+4725x^44+6102x^45+3465x^46+2498x^47+1016x^48+582x^49+287x^50+110x^51+59x^52+14x^53+9x^54+6x^55+3x^56+3x^58+2x^59

The gray image is a code over GF(2) with n=352, k=15 and d=148.
This code was found by Heurico 1.16 in 7.93 seconds.