The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+212x^28+8x^29+322x^30+88x^31+727x^32+840x^33+1604x^34+2136x^35+4520x^36+2136x^37+1608x^38+840x^39+752x^40+88x^41+284x^42+8x^43+160x^44+22x^46+24x^48+4x^52

The gray image is a code over GF(2) with n=288, k=14 and d=112.
This code was found by Heurico 1.16 in 3.34 seconds.