The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+59x^28+70x^29+90x^30+170x^31+218x^32+564x^33+925x^34+1240x^35+1563x^36+1240x^37+896x^38+596x^39+170x^40+156x^41+102x^42+40x^43+33x^44+18x^45+30x^46+2x^47+3x^48+5x^50+1x^52

The gray image is a code over GF(2) with n=288, k=13 and d=112.
This code was found by Heurico 1.16 in 0.785 seconds.