The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  8  8  1  0  1  2  1  1  4  2  1 12  1  2  1  1  8  1  1  1  1  4  2  2  2  4
 0  2  0  6  0  6  0  2  4  6 12 12 14 10  2  4  6  6  2  2 14  2 14 14  8  0  2  2  8  2  6 14  2  6  4  0  8  4  4  4 12  4  6 12
 0  0 12  0  0  4  4  4  4  0  8 12  4  4  8  0  4  0 12  0  8  8 12  8  8  8  8  0 12  8 12  4  4  8  0  4  4  0  8 12  8 12 12  4
 0  0  0 12 12  4  4  0  8  8  8 12  8  4 12  4 12  8  0  4  4  0  0  4  4  0 12  4  8  8  4  0  0  0 12  4  8 12  4  8 12  8  4 12
 0  0  0  0  8  0  0  0  8  8  8  8  0  0  0  0  8  0  8  8  0  0  8  0  8  0  0  8  0  8  8  0  8  0  8  8  8  8  0  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  0  8  8  0  8  0  8  0  0  8  0  8  0  8  0  8  8  8  0  8  8  0  0  0  0  8  0  8  8
 0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  8  0  0  8  0  8  8  0  0  8  8  8  8  8  8  0  0  0  0  8  0  8  8  8  0  8  8  0  8
 0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  8  8  0  0  0  8  8  8  0  0  0  0  8  8  0  8  8  8  0  8  8  8  8  0  8  8  0  0

generates a code of length 44 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+66x^35+155x^36+300x^37+476x^38+878x^39+1458x^40+2308x^41+3634x^42+4532x^43+5008x^44+4740x^45+3615x^46+2468x^47+1411x^48+764x^49+422x^50+218x^51+141x^52+80x^53+36x^54+30x^55+18x^56+8x^58+1x^62

The gray image is a code over GF(2) with n=352, k=15 and d=140.
This code was found by Heurico 1.16 in 19.5 seconds.