The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+56x^20+25x^22+20x^23+128x^24+96x^25+176x^26+160x^27+408x^28+224x^29+5579x^30+264x^31+363x^32+160x^33+272x^34+64x^35+64x^36+32x^37+71x^38+4x^39+4x^40+16x^42+5x^46

The gray image is a code over GF(2) with n=240, k=13 and d=80.
This code was found by Heurico 1.16 in 0.509 seconds.