The generator matrix

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

generates a code of length 30 over Z16 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+12x^21+78x^22+88x^23+189x^24+246x^25+433x^26+1124x^27+1311x^28+2612x^29+4145x^30+2628x^31+1381x^32+1160x^33+410x^34+236x^35+158x^36+64x^37+48x^38+20x^39+29x^40+2x^41+5x^42+3x^44+1x^46

The gray image is a code over GF(2) with n=240, k=14 and d=84.
This code was found by Heurico 1.16 in 37.3 seconds.