The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+57x^26+62x^27+234x^28+254x^29+525x^30+406x^31+1225x^32+1612x^33+2593x^34+7888x^35+2953x^36+7912x^37+2681x^38+1664x^39+1269x^40+404x^41+483x^42+194x^43+188x^44+58x^45+55x^46+26x^47+16x^48+3x^50+1x^52+3x^54+1x^56

The gray image is a code over GF(2) with n=288, k=15 and d=104.
This code was found by Heurico 1.16 in 11.3 seconds.