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  2  2  1  1  1  1  1  2  1  1  1  2  1  2  1  1
 0  8  0  0  0  0  0  0  0  0  8  8  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  8  8  0  8  8  0  8  8  8  0  8  0  0  8  8  0
 0  0  8  0  0  0  0  0  0  8  8  8  0  8  8  0  0  0  8  8  8  8  8  8  0  8  0  0  0  0  0  0  8  8  8  0  8  8  8  0  8  0  0
 0  0  0  8  0  0  0  0  0  8  0  8  8  8  0  8  0  8  8  0  0  0  0  0  8  0  8  8  0  8  0  8  8  0  8  0  0  8  0  8  0  8  0
 0  0  0  0  8  0  0  0  8  0  0  8  8  0  8  8  0  0  8  8  0  0  0  8  8  8  8  0  0  0  8  8  0  0  8  0  8  0  0  8  8  0  0
 0  0  0  0  0  8  0  0  8  0  8  0  0  8  8  8  0  8  8  0  0  0  0  8  8  0  0  8  8  8  0  0  0  8  8  0  8  8  8  8  0  0  8
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  8  0  0  8  0  0  8  0  8  0  8  8  0  8  8  0  0  0  0  8  0  8  8  8  8  8  0
 0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  0  8  0  8  0  0  8  8  0  0  0  8  8  0  0  0  8  0  8  8  0  8  0  8  8  8  8  0

generates a code of length 43 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+63x^36+8x^38+106x^40+80x^42+1536x^43+117x^44+40x^46+61x^48+27x^52+8x^56+1x^76

The gray image is a code over GF(2) with n=344, k=11 and d=144.
This code was found by Heurico 1.16 in 0.11 seconds.