The generator matrix

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

generates a code of length 29 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+90x^24+112x^26+192x^27+193x^28+896x^29+160x^30+192x^31+144x^32+48x^34+14x^36+4x^40+1x^44+1x^48

The gray image is a code over GF(2) with n=232, k=11 and d=96.
This code was found by Heurico 1.16 in 0.0534 seconds.