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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+122x^40+64x^41+112x^42+384x^43+224x^44+64x^45+16x^46+28x^48+8x^52+1x^80

The gray image is a code over GF(2) with n=344, k=10 and d=160.
This code was found by Heurico 1.16 in 1.5 seconds.