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

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

Homogenous weight enumerator: w(x)=1x^0+123x^36+16x^37+40x^38+128x^39+357x^40+736x^41+336x^42+128x^43+106x^44+16x^45+8x^46+41x^48+11x^52+1x^72

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 2.33 seconds.