The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+117x^24+62x^26+235x^28+8x^29+126x^30+72x^31+400x^32+288x^33+332x^34+672x^35+519x^36+1008x^37+25088x^38+1008x^39+429x^40+672x^41+484x^42+288x^43+257x^44+72x^45+344x^46+8x^47+75x^48+140x^50+13x^52+40x^54+2x^56+6x^58+2x^62

The gray image is a code over GF(2) with n=304, k=15 and d=96.
This code was found by Heurico 1.16 in 11.5 seconds.