The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+51x^26+32x^27+99x^28+90x^29+156x^30+206x^31+429x^32+576x^33+808x^34+5232x^35+1003x^36+5252x^37+829x^38+572x^39+426x^40+208x^41+163x^42+96x^43+65x^44+18x^45+38x^46+6x^47+22x^48+2x^50+1x^52+1x^54+2x^56

The gray image is a code over GF(2) with n=288, k=14 and d=104.
This code was found by Heurico 1.16 in 28.1 seconds.