The generator matrix

 1  0  1  1  1 14  1  1  6  1  8  1  1  1  1 12  1  2  1 10  1  1  1  4  1 14  2  1  1  2  1  0  1  1
 0  1 11 14  5  1  0  3  1  6  1 13 12 15 10  1  9  1  7  1  1  0  6  1  3  1  1 14  8 14  8  1  8  0
 0  0 12  4  0  4 12  0  0  8 12  4  0  8  0  0  8  4  4  0  4  0  8 12  0 12  4 12  4  4  4  0  4  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  8  0  8  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  0  0  8  0  8  8  0  0  8  0  8  8  0  8  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  0  8  8  8  0  8  8  0  8  8  0  0  0  8  8  8  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  8  8  0  8  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  8  0  8  0  0  8  0  8  8  8  8  0  8  0  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  8  0  8  8  8  8  8  0  8  8  0  8  0  0  0  0  8  8  0  0  0  0  0

generates a code of length 34 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+25x^24+40x^25+78x^26+174x^27+303x^28+680x^29+1126x^30+5270x^31+5779x^32+14308x^33+9945x^34+14328x^35+5830x^36+5284x^37+1073x^38+664x^39+317x^40+164x^41+56x^42+42x^43+27x^44+4x^45+8x^46+2x^47+6x^48+1x^50+1x^54

The gray image is a code over GF(2) with n=272, k=16 and d=96.
This code was found by Heurico 1.16 in 17.6 seconds.