The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  0  1  1  2 12  1  1  2  1  1  0  1  2  1  1  1  0  1  1  2  2  1  2  1  1
 0  2 12  6  0  6 12 10  0  6  6  2 12 10 10  2  0  6  6 12 10  2 12 10 10 12  0  2  0  0  6  6  0  0  6  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  8  8  8  0  0  0  0  0  8  8  0  0  8  8
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  0  8  8  8  8  8  0  8
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  8  8  0  8  0  8  0  0  0  8  8  0  0  8  8  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  0  0  8  0  0  8  8  0  0  8  0  8  0  8  0  0  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  8  0  8  8  0  8  0  8  0  0  8
 0  0  0  0  0  0  0  8  0  0  8  0  8  8  8  8  8  8  8  8  8  8  8  0  0  8  0  0  8  8  8  0  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  0  0  8  8  8  0  0  8  8  8  8  8  0  8  8  0  0  0  0  8  8
 0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  0  8  0  8  0  8  8  8  8  8  8  0  0  0  0  0  0  0  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+66x^26+6x^27+144x^28+80x^29+274x^30+418x^31+1057x^32+1800x^33+3760x^34+5876x^35+5802x^36+5896x^37+3745x^38+1820x^39+1048x^40+408x^41+295x^42+70x^43+116x^44+8x^45+44x^46+2x^47+22x^48+6x^50+2x^52+1x^54+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 14.8 seconds.