The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1 12  1  1  6  0  1  6  2  2  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  6  5  1 15  1  3 12  1  1  0  1  0  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  8  8  8  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  8  8  0  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  8  0  8  8  8  0  8  8  8  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  8  0  8  0  0  0  8  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  0  8  8  8  0  0  8  0  8  0  0  0  0  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  0  8  8  8  8  8  8  0  8  0  8  8  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  0  0  0  0  8  8  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+69x^20+8x^21+58x^22+112x^23+363x^24+656x^25+864x^26+3440x^27+6945x^28+14048x^29+11972x^30+14288x^31+7086x^32+3696x^33+880x^34+592x^35+319x^36+24x^37+50x^38+53x^40+11x^44+1x^48

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 12.7 seconds.