The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^20+8x^21+81x^22+64x^23+124x^24+168x^25+485x^26+312x^27+3405x^28+472x^29+6042x^30+472x^31+3456x^32+312x^33+490x^34+168x^35+104x^36+64x^37+53x^38+8x^39+34x^40+17x^42+5x^44+1x^48

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 2.07 seconds.