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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+34x^36+232x^37+305x^38+432x^39+129x^40+388x^41+245x^42+204x^43+40x^44+20x^45+8x^46+4x^47+1x^50+1x^54+4x^56

The gray image is a code over GF(2) with n=320, k=11 and d=144.
This code was found by Heurico 1.16 in 0.0639 seconds.