The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  0  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  0  8  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  0  0  0  0  0  8  8  8  0  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  8  8  0  0  0  0  0  0  8  8  0  0  8  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  0  8  0  8  0  8  0  0  0  8  8  8  0  8  0  0  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  0  0  8  0  0  8  0  0  0  0  8  8  0  0  0  8  8  0  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  0  8  0  8  0  0  8  0  0  0  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  8  0  8  8  0  0  8  0  8  8  0  0  0  0  0  8  0  0  8  0  0  0
 0  0  0  0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  8  0  8  0  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  8  0  0  0  8  0  0  0  8  0  0  8  8  0  8  8  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  0  0  8  0  8  0  8  8  8  0  8  0  0  8  8  0  0  0  0  0  0  0  0

generates a code of length 39 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+144x^24+260x^28+91x^30+505x^32+224x^33+126x^34+224x^35+476x^36+1120x^37+398x^38+25696x^39+440x^40+672x^41+534x^42+672x^43+156x^44+32x^45+532x^46+32x^47+62x^48+218x^50+4x^52+130x^54+18x^58+1x^62

The gray image is a code over GF(2) with n=312, k=15 and d=96.
This code was found by Heurico 1.16 in 11.5 seconds.