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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+141x^44+40x^46+64x^47+81x^48+1408x^49+80x^50+64x^51+98x^52+8x^54+45x^56+17x^60+1x^88

The gray image is a code over GF(2) with n=392, k=11 and d=176.
This code was found by Heurico 1.16 in 85.2 seconds.