The generator matrix

 1  0  1  1  1 14  1  1  6  1  1  8  1  1  1  1  4  1  1  1  1 10  8  0 14  4  2  2  1  1
 0  1 11 14  5  1  0  3  1  6 13  1  4 10  7  9  1  6  5  8 11  1  4  1  1  8  8  8  0  0
 0  0 12  4  0  4 12  0  0  8  4 12  4  0  4  0  4  0  8  4  4  0  4  8  4  4  4  4  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  0  0  8  0  8  8  8  0  8  8  0  0  0  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  0  8  0  0  8  8  8  0  8  8  0  8  8  8  0  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  8  8  8  0  0  8  8  8  0  8  0  8  0  0  0  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  8  0  0  0  8  8  8  8  0  8  8  0  0
 0  0  0  0  0  0  0  0  8  8  8  0  8  0  8  8  8  0  0  0  8  0  8  0  0  0  0  8  0  0

generates a code of length 30 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+68x^20+194x^22+701x^24+384x^25+3480x^26+1920x^27+11540x^28+5888x^29+17228x^30+5888x^31+11475x^32+1920x^33+3480x^34+384x^35+724x^36+194x^38+62x^40+4x^44+1x^56

The gray image is a code over GF(2) with n=240, k=16 and d=80.
This code was found by Heurico 1.16 in 13.4 seconds.