The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+153x^24+76x^26+503x^28+64x^29+540x^30+640x^31+2438x^32+1984x^33+8408x^34+2816x^35+8993x^36+1984x^37+2008x^38+640x^39+909x^40+64x^41+220x^42+257x^44+12x^46+49x^48+7x^52+2x^56

The gray image is a code over GF(2) with n=280, k=15 and d=96.
This code was found by Heurico 1.16 in 10.2 seconds.