The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  2  1  2  1  2  1  2  1  2
 0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  8  8  0  8  8  0  8  8  0  8  8  0
 0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  0  0  8  0  0  8  0  8  8  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  0  8  8  0  8  8  8  8  0  0  0  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  0  0  0  8  8  8  0  8  0  8  8  0  8  8
 0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  0  8  8  0  8  8  8  0  0  0  8  0  0  0  8  0  8  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  8  0  0  8  8  8  8  0
 0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+89x^28+16x^30+177x^32+112x^34+3330x^36+112x^38+149x^40+16x^42+69x^44+24x^48+1x^56

The gray image is a code over GF(2) with n=288, k=12 and d=112.
This code was found by Heurico 1.16 in 0.361 seconds.