The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+108x^24+48x^26+412x^28+32x^29+486x^30+480x^31+1645x^32+1952x^33+2042x^34+7776x^35+2837x^36+7776x^37+1996x^38+1952x^39+1646x^40+480x^41+500x^42+32x^43+419x^44+46x^46+86x^48+2x^50+11x^52+2x^56+1x^60

The gray image is a code over GF(2) with n=288, k=15 and d=96.
This code was found by Heurico 1.16 in 10.1 seconds.