The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  0  1  2  1  1  2  1 12  2  2  1  2 12  1  1  2  0
 0  2  0  6  4  6 12  2  8  0  6 14  4  4  2 10  6  2 14  2  8  6 14 12 10  6  2  2  6  8 10  2  6 10  8  2
 0  0 12  0  4  0  0  8  0  4  4 12  8  4 12 12  8  0  8  8  0  4 12  0 12  4  8  8  4  8  4  8 12  0  8 12
 0  0  0 12  0  0  8  4  4  4  4  8 12  4  0  4  0 12  4  8 12 12  0  8 12  4  0 12  8 12  8  8  4  0 12  4
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  8  8  8  8  8  8  0  0  0  0  8  0  0  0  8  8  0  0  8  8  8

generates a code of length 36 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+82x^31+164x^32+304x^33+654x^34+644x^35+480x^36+658x^37+574x^38+278x^39+134x^40+60x^41+18x^42+16x^43+16x^44+2x^45+2x^46+4x^47+5x^48

The gray image is a code over GF(2) with n=288, k=12 and d=124.
This code was found by Heurico 1.16 in 0.21 seconds.