The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^28+88x^29+234x^30+298x^31+711x^32+1120x^33+2012x^34+2024x^35+3180x^36+2206x^37+2084x^38+1060x^39+688x^40+278x^41+192x^42+72x^43+36x^44+18x^45+18x^46+2x^47+8x^48+2x^49+4x^50

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 2.59 seconds.