The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  2  1  2  1  1  1  2  1  2  1  0
 0  2  0  2  8  0  6  6  4 12  4  6 10  2  4  6 10  2 14  2  0  4 14  4  0  8 12 10 10  2
 0  0  2  2  4  6  6  0 12  8  2  4  6  4 14  6 14  6  8  2  2  2 10  6  8  2  8 14  4 14
 0  0  0  8  8  8  0  8  0  8  0  8  8  0  8  8  0  8  0  0  8  0  0  0  8  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+244x^27+166x^28+460x^29+448x^30+340x^31+142x^32+176x^33+52x^35+10x^36+4x^37+4x^39+1x^48

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 6.22 seconds.