The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+122x^38+618x^39+1444x^40+2700x^41+3556x^42+5186x^43+5537x^44+5246x^45+3869x^46+2434x^47+1117x^48+604x^49+192x^50+94x^51+25x^52+6x^53+3x^54+4x^55+4x^56+4x^57+2x^58

The gray image is a code over GF(2) with n=352, k=15 and d=152.
This code was found by Heurico 1.16 in 6.31 seconds.