The generator matrix

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

generates a code of length 29 over Z16 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+49x^18+109x^20+148x^22+190x^24+128x^25+226x^26+512x^27+281x^28+13056x^29+290x^30+512x^31+263x^32+128x^33+226x^34+143x^36+72x^38+26x^40+10x^42+11x^44+2x^46+1x^50

The gray image is a code over GF(2) with n=232, k=14 and d=72.
This code was found by Heurico 1.16 in 1.87 seconds.