The generator matrix

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

generates a code of length 29 over Z16 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+128x^16+53x^18+262x^20+142x^22+430x^24+256x^25+390x^26+1024x^27+630x^28+26112x^29+622x^30+1024x^31+415x^32+256x^33+472x^34+130x^36+250x^38+50x^40+106x^42+2x^44+10x^46+3x^50

The gray image is a code over GF(2) with n=232, k=15 and d=64.
This code was found by Heurico 1.16 in 4.86 seconds.