The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^20+48x^21+183x^22+218x^23+355x^24+576x^25+844x^26+1120x^27+1608x^28+6200x^29+10216x^30+6244x^31+1689x^32+1176x^33+904x^34+560x^35+316x^36+184x^37+119x^38+50x^39+59x^40+8x^41+20x^42+8x^44+2x^46

The gray image is a code over GF(2) with n=240, k=15 and d=80.
This code was found by Heurico 1.16 in 7.42 seconds.