The generator matrix

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

generates a code of length 30 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+26x^22+108x^23+241x^24+484x^25+974x^26+2488x^27+2543x^28+7164x^29+4669x^30+7160x^31+2645x^32+2492x^33+952x^34+472x^35+190x^36+100x^37+32x^38+12x^39+9x^40+2x^42+3x^44+1x^46

The gray image is a code over GF(2) with n=240, k=15 and d=88.
This code was found by Heurico 1.16 in 5.89 seconds.