The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+80x^38+298x^39+675x^40+1314x^41+1763x^42+2786x^43+2683x^44+2768x^45+1767x^46+1220x^47+584x^48+254x^49+91x^50+42x^51+21x^52+12x^53+9x^54+6x^55+4x^56+4x^57+2x^58

The gray image is a code over GF(2) with n=352, k=14 and d=152.
This code was found by Heurico 1.16 in 2.01 seconds.