The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+59x^24+54x^26+6x^27+218x^28+60x^29+237x^30+206x^31+653x^32+464x^33+1668x^34+2860x^35+7349x^36+5096x^37+7340x^38+2860x^39+1683x^40+464x^41+677x^42+206x^43+220x^44+60x^45+205x^46+6x^47+52x^48+46x^50+5x^52+10x^54+3x^58

The gray image is a code over GF(2) with n=296, k=15 and d=96.
This code was found by Heurico 1.16 in 10.1 seconds.