The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+43x^26+74x^27+186x^28+258x^29+375x^30+574x^31+798x^32+2016x^33+3145x^34+5236x^35+7219x^36+5300x^37+3238x^38+2060x^39+871x^40+560x^41+301x^42+226x^43+120x^44+58x^45+59x^46+22x^47+17x^48+7x^50+3x^52+1x^56

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 seconds.