The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+28x^34+44x^35+141x^36+162x^37+233x^38+330x^39+411x^40+860x^41+1779x^42+2692x^43+2993x^44+2704x^45+1836x^46+880x^47+427x^48+324x^49+170x^50+144x^51+95x^52+46x^53+41x^54+6x^55+25x^56+7x^58+3x^60+2x^62

The gray image is a code over GF(2) with n=352, k=14 and d=136.
This code was found by Heurico 1.16 in 4.35 seconds.