The generator matrix

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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+74x^36+42x^38+16x^39+267x^40+32x^41+438x^42+176x^43+1110x^44+1344x^45+1312x^46+1264x^47+1078x^48+160x^49+440x^50+80x^51+199x^52+70x^54+59x^56+2x^58+24x^60+3x^64+1x^68

The gray image is a code over GF(2) with n=368, k=13 and d=144.
This code was found by Heurico 1.16 in 1.2 seconds.