The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+124x^24+202x^26+740x^28+1476x^30+1024x^31+4473x^32+3072x^33+10444x^34+3072x^35+4602x^36+1024x^37+1536x^38+684x^40+154x^42+112x^44+12x^46+14x^48+2x^52

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 9.68 seconds.