The generator matrix

 1  0  1  1  1 14  1  1  2  1  1  6  1  1 12  1  8  1 10  1  1  1  1  4  1  1  1  1  1  1  1  1  1  1 12  1  8  2  1  1  1  1  1  1
 0  1 11  6  5  1  8  7  1  4  3  1 10  9  1 14  1 13  1 15  4 10  1  1 12  2  0 14  6  0  6  0  8  3  1  3  1 10  8  4  1  7 14  0
 0  0 12  0  8  4  4  4 12 12  8  0  0  8  0  4  4  4  0  8  4  0 12 12  0 12  8 12  4 12  8  0  8  0  8 12  4  8 12  4  4  4  0  0
 0  0  0  8  8  8  0  8  0  8  0  8  0  0  8  0  8  0  0  8  8  8  8  0  0  0  8  8  8  0  0  8  0  8  0  8  0  8  8  0  0  0  8  0

generates a code of length 44 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+73x^40+160x^41+373x^42+230x^43+398x^44+228x^45+361x^46+136x^47+68x^48+12x^49+2x^51+4x^56+1x^62+1x^66

The gray image is a code over GF(2) with n=352, k=11 and d=160.
This code was found by Heurico 1.16 in 0.0811 seconds.