The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+74x^27+994x^28+3018x^29+7832x^30+16602x^31+31401x^32+43534x^33+53266x^34+45864x^35+32278x^36+16038x^37+7398x^38+2588x^39+918x^40+258x^41+46x^42+22x^43+8x^44+2x^46+2x^47

The gray image is a code over GF(2) with n=272, k=18 and d=108.
This code was found by Heurico 1.16 in 261 seconds.