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  2  4  1  1  1  1  2  1  2  1  2  4  2
 0 12  0  4  0  0  4  4  8  8  4 12 12 12  0  8  0  4 12 12  0  4  8  0  8  0  0  8 12 12  0 12 12  8 12 12 12  4  8  0  0
 0  0 12  4  0 12 12  0  8  4  4  0  8  4  8 12  0 12  4  0  8  0  4 12  4  4  0  8  8  0  8 12 12  8  0  0  0  8  4 12  0
 0  0  0  8  0  0  8  0  0  0  0  8  8  0  8  8  8  8  0  0  8  8  8  8  8  0  0  8  0  8  0  0  8  0  0  0  8  8  8  8  0
 0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  0  8  0  8  0  0  8  0  0  8  8  8  0  0  8  8  8  8  8  8  8  8  8  8  0
 0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  0  8  0  8  8  0  8  8  0  0  8  8  8  8  8  0  0  8  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+125x^36+16x^37+52x^38+192x^39+356x^40+608x^41+290x^42+192x^43+126x^44+16x^45+34x^46+27x^48+6x^50+4x^52+2x^54+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 4.34 seconds.