The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1  1  1 12  1  1  1  1  6  2  0  0  0  0  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  5  1  6  3  1 12 10 15  9  1  0  3  6  5  1  6  1  1  1  1  0
 0  0  8  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  8  0  8  8  8  0  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  0  8  8  0  8  8  0  8  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  0  8  8  0  8  8  8  0  8  8  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  8  0  0  8  8  8  8  8  0  0  0  8  0  8  8  0  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  0  8  8  8  0  8  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  8  8  8  8  0  8  0  8  0  0  0  0  8  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  8  0  0  0  0  8  0  8  8  0  0  8  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+36x^24+12x^25+39x^26+24x^27+300x^28+156x^29+1238x^30+1324x^31+4840x^32+4612x^33+7573x^34+4652x^35+4832x^36+1332x^37+1297x^38+132x^39+218x^40+32x^41+73x^42+12x^43+12x^44+16x^46+1x^48+3x^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 4.57 seconds.