The generator matrix

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

generates a code of length 41 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+40x^36+192x^37+386x^38+476x^39+554x^40+744x^41+748x^42+496x^43+232x^44+76x^45+72x^46+52x^47+5x^48+8x^49+4x^50+4x^53+6x^54

The gray image is a code over GF(2) with n=328, k=12 and d=144.
This code was found by Heurico 1.16 in 0.159 seconds.