The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^20+180x^22+32x^23+610x^24+352x^25+1086x^26+2336x^27+2552x^28+5472x^29+7176x^30+5472x^31+2663x^32+2336x^33+1132x^34+352x^35+590x^36+32x^37+148x^38+102x^40+6x^42+12x^44

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 7.24 seconds.