The generator matrix

 1  1  1  1  1  1  1  1  2  0  1  1  2  1  1 12  1  1  1  1  2  1  2  2  1  2  2  1  1  1
 0  2 12  6  0  6 12 10  6  2  0  6 10 12 10  2  0  6 12 10  0  0  6  6 12  6  6  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  8  8  0  0  0  0  0  0  0  8  8
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  0  0  0  0  8  0  8  0  8  8
 0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  0  0  8  8  0  0  0  8  8  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  8  0  0  8  8  0  8  8  8  0  8  8  0  8  0  0  0
 0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  0  8  8  0  0  0  0  8  0  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  0  8  0  0  8  0  8  8  8  0  0  8  0  0  8
 0  0  0  0  0  0  0  0  8  8  0  0  8  0  0  8  8  8  8  8  0  0  8  8  8  0  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+24x^20+8x^21+55x^22+60x^23+120x^24+184x^25+439x^26+728x^27+1380x^28+4056x^29+2090x^30+4320x^31+1407x^32+584x^33+434x^34+264x^35+124x^36+32x^37+47x^38+4x^39+8x^40+7x^42+8x^44

The gray image is a code over GF(2) with n=240, k=14 and d=80.
This code was found by Heurico 1.16 in 1.54 seconds.