The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^24+64x^25+179x^26+232x^27+335x^28+598x^29+829x^30+1532x^31+3188x^32+5746x^33+7199x^34+5784x^35+3162x^36+1572x^37+851x^38+576x^39+356x^40+204x^41+141x^42+64x^43+55x^44+6x^45+15x^46+4x^47+5x^48+2x^49+1x^50+1x^54

The gray image is a code over GF(2) with n=272, k=15 and d=96.
This code was found by Heurico 1.16 in 9.91 seconds.