The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  2  1  2  1  1  1
 0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  8  8  0  8  0  8  0  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  0  0  8  0  0  8  0  0  8  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  0  8  8  0  8  8  0  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  0  0  0  8  8  8  8  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  8  0  8  8  8  0  0  8  8  8  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  0  8  8  0  8  8  8  0  8  0  0  0  0  8  8  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  0  8  8  8  8  8  8  0  8  0  0  0  0  0  8  8  0
 0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  0  0  8  8  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+33x^24+20x^26+4x^27+76x^28+28x^29+48x^30+84x^31+57x^32+140x^33+3134x^34+140x^35+44x^36+84x^37+57x^38+28x^39+29x^40+4x^41+52x^42+16x^44+14x^46+2x^50+1x^54

The gray image is a code over GF(2) with n=272, k=12 and d=96.
This code was found by Heurico 1.16 in 0.21 seconds.