The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+54x^26+66x^27+208x^28+280x^29+386x^30+432x^31+659x^32+1020x^33+2645x^34+6362x^35+8459x^36+6370x^37+2666x^38+1126x^39+726x^40+458x^41+323x^42+188x^43+176x^44+62x^45+60x^46+18x^47+6x^48+2x^49+9x^50+5x^52+1x^58

The gray image is a code over GF(2) with n=288, k=15 and d=104.
This code was found by Heurico 1.16 in 11.4 seconds.