The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^24+54x^26+423x^28+64x^29+560x^30+832x^31+2321x^32+2176x^33+3372x^34+2176x^35+2300x^36+832x^37+576x^38+64x^39+424x^40+46x^42+76x^44+6x^48+1x^60

The gray image is a code over GF(2) with n=272, k=14 and d=96.
This code was found by Heurico 1.16 in 2.68 seconds.