The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+163x^20+80x^22+588x^24+832x^26+1024x^27+3291x^28+7168x^29+6368x^30+7168x^31+3453x^32+1024x^33+832x^34+553x^36+80x^38+116x^40+25x^44+2x^48

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 8.11 seconds.