The generator matrix

 1  0  1  1  1 14  1  1  2  1  1  6  1  1 12  1  8  1  1  1  1  1  2  1  1  1  1  1  1  2
 0  1 11  6  5  1  8  7  1  4  3  1 10  9  1 14  1 13  1 15 11  9 10 14  0 11  1  5  5  0
 0  0 12  0  8  4  4  4 12 12  8  0  0  8  0  4  4  4 12  8 12  0  8 12  0  8  4  0 12 12
 0  0  0  8  8  8  0  8  0  8  0  8  0  0  8  0  8  0  0  8  8  0  8  8  8  8  8  8  8  8

generates a code of length 30 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+200x^27+246x^28+418x^29+288x^30+536x^31+214x^32+86x^33+16x^34+32x^35+1x^36+6x^37+1x^40+2x^41+1x^44

The gray image is a code over GF(2) with n=240, k=11 and d=108.
This code was found by Heurico 1.16 in 3.1 seconds.