The generator matrix

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

generates a code of length 29 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+117x^20+80x^22+453x^24+256x^25+992x^26+1024x^27+4537x^28+1536x^29+4320x^30+1024x^31+1298x^32+256x^33+224x^34+207x^36+16x^38+39x^40+3x^44+1x^48

The gray image is a code over GF(2) with n=232, k=14 and d=80.
This code was found by Heurico 1.16 in 2.14 seconds.