The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+12x^25+68x^26+82x^27+184x^28+242x^29+294x^30+724x^31+1248x^32+1828x^33+4738x^34+3196x^35+7377x^36+3308x^37+4804x^38+1888x^39+1270x^40+700x^41+272x^42+226x^43+130x^44+50x^45+54x^46+28x^47+25x^48+4x^49+10x^50+5x^52

The gray image is a code over GF(2) with n=288, k=15 and d=100.
This code was found by Heurico 1.16 in 54.6 seconds.