The generator matrix

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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+31x^34+26x^35+137x^36+108x^37+214x^38+234x^39+459x^40+506x^41+1194x^42+2256x^43+2455x^44+5074x^45+7388x^46+5028x^47+2504x^48+2260x^49+1170x^50+554x^51+476x^52+224x^53+198x^54+82x^55+91x^56+18x^57+34x^58+12x^59+19x^60+2x^61+8x^62+1x^64+3x^66+1x^68

The gray image is a code over GF(2) with n=368, k=15 and d=136.
This code was found by Heurico 1.16 in 16 seconds.