The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  2  2  1  1  2  1  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  8  8  0  8
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  0  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  0  0  8  0  0  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  0  8  0  8  8  8  0  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  8  8  0  0  0  8  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  0  8  0  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  0  0  0  8  0  8  0  0  8  8  8  8  8  0
 0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  0  0  8  8  0  0  8  8  0  0  0  0  8  8
 0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  8  0  0  8  8  8  8  0  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+158x^20+371x^24+192x^26+978x^28+12928x^30+1056x^32+192x^34+378x^36+105x^40+22x^44+3x^48

The gray image is a code over GF(2) with n=240, k=14 and d=80.
This code was found by Heurico 1.16 in 2.37 seconds.