The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12 10  1  1  1  1  1  1  0  1  1  6 12  1  1  0  1  1 10  1  2  4  1  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5  1  1 12 10 15  9  3  0  1  5  6  1  1 12 10  1 15  9  1  0  6  0  6  6  0  3  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  8  8  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  8  8  0  8
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  0  8  8  8  0  0  0  8  0  0  8  8  8  8  8  8  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  8  0  8  8  8  8  8  8  0  0  8  8  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  8  0  8  0  8  0  8  8  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  0  8  8  0  8  0  8  0  0  0  8  8  8  8  0  8  8  0  0  0  8  8  8  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  8  8  8  8  8  8  0  8  8  8  8  0  0  0  8  8  0  0  0  8  8  0  0  0  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  0  8  8  0  0  8  8  8  8  0  0  8  0  0  8  0  0  8  8  8  8  8  8  8  8
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  0  8  8  0  0  8  8  8  0  0  8  0  0  0  0  0  8  0  8  8  8  0  0  8  8  0

generates a code of length 45 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+53x^34+4x^35+140x^36+32x^37+371x^38+276x^39+1175x^40+2112x^41+5425x^42+6376x^43+12271x^44+9024x^45+12327x^46+6376x^47+5475x^48+2112x^49+1127x^50+276x^51+343x^52+32x^53+129x^54+4x^55+37x^56+19x^58+13x^60+5x^62+1x^68

The gray image is a code over GF(2) with n=360, k=16 and d=136.
This code was found by Heurico 1.16 in 29 seconds.