The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  1  2  1  2  4  1  4  1  8  2  1  1  4  1  2  1  1  4  2  2  1  1  1
 0 12  0  4  0  0  4 12  0  0  4  4  8  8  4  4  8  8  8  4 12 12  0  8  4  0  4  4  0  4 12  0 12 12 12  0 12  0  4 12  8  8  0  0
 0  0 12  4  0 12  4  0  0 12 12  0  8  4  4  8 12  4  8  4  0  0 12  4  4 12 12  4  0 12  8  4  8  0  4 12  0  0 12  8  4  4  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  0  0  8  0  8  8  0  0  0  8  0  8  8  8  0  8  0  8  0  0  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  0  0  8  8  8  0  8  8  0  8  0  8  0  8  8  0  0  0  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  0  8  0  8  0  8  8  0  8  8  8  8  0  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  0  8  8  0  8  0  8  8  8  0  8  0  0  0  8  0  8  8  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  0  8  8  0  0  0  0  0  0  8  8  8  0  8  0  0  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  0  0  8  0  0  8  8  0  8  8  0  8  8  8  0  8  8  8  8  8  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  8  8  0  0  8  0  8  8  0  8  8  8  0  0  0  0  8  8  0  0  0  8  8  0  0  8  0  0

generates a code of length 44 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+91x^32+174x^34+477x^36+16x^37+676x^38+176x^39+1447x^40+2192x^41+1966x^42+7856x^43+2589x^44+7856x^45+2024x^46+2192x^47+1453x^48+176x^49+698x^50+16x^51+463x^52+84x^54+109x^56+10x^58+23x^60+3x^64

The gray image is a code over GF(2) with n=352, k=15 and d=128.
This code was found by Heurico 1.16 in 14.9 seconds.