The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  8  1  1  2  0  1  1  2  2  2  2  8  1  1  2  1  4  1
 0  2  0  6  0 14  0  6 14  4  6  2  6  8  6  2  4 10  6 10  2  8  2  0 10  2 14  8  0
 0  0 12  0  0  0 12  4 12  8  0  8  4  4 12 12 12  0 12  4  4 12  0  0  0  8  8  8  4
 0  0  0 12  0  0  0  0  0  0  8  8  4  4  4  4  8 12  0 12  4  8  8  4  0  4  4 12  0
 0  0  0  0 12  4 12 12  8 12  0  4  0 12  8  8  0 12 12  8  4 12  4 12  4  8  4  0  4
 0  0  0  0  0  8  8  8  0  8  8  8  0  0  8  0  8  0  0  0  0  8  0  8  0  0  8  8  0

generates a code of length 29 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+84x^22+48x^23+411x^24+400x^25+1162x^26+1616x^27+2903x^28+3040x^29+3014x^30+1616x^31+1226x^32+400x^33+296x^34+48x^35+97x^36+18x^38+2x^40+2x^42

The gray image is a code over GF(2) with n=232, k=14 and d=88.
This code was found by Heurico 1.16 in 1.96 seconds.