The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  1  4  2  4  1  1  1  1
 0 12  0  0  0  4 12 12  8  8  0  0  4  4  4 12  8  4 12  4 12  8  8 12  8  8  4  0  4  4  4  4 12 12 12 12  4  0  4  8  8
 0  0 12  0  4  4  4  0  8  0  4 12  4  4  0  8  0 12  4  8  4  8  8  8 12  0 12 12  0  4  0  4  8 12  0  4  8  0  0  8  0
 0  0  0 12  4  8  4  4  0  4  4  0  0 12  4  8  4  0  8  0 12  4  0  4 12 12  8  8 12  0  8  8  8  4  0  0 12 12  0 12  4
 0  0  0  0  8  8  0  8  8  8  0  8  0  8  0  8  0  8  8  8  8  8  0  0  8  8  0  8  8  8  8  0  0  0  8  0  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+94x^36+4x^37+150x^38+128x^39+431x^40+504x^41+410x^42+128x^43+87x^44+4x^45+58x^46+20x^48+22x^50+6x^52+1x^68

The gray image is a code over GF(2) with n=328, k=11 and d=144.
This code was found by Heurico 1.16 in 0.101 seconds.