The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+228x^31+298x^32+362x^33+329x^34+382x^35+236x^36+130x^37+22x^38+44x^39+7x^40+2x^41+1x^42+2x^43+2x^44+2x^45

The gray image is a code over GF(2) with n=272, k=11 and d=124.
This code was found by Heurico 1.16 in 61.3 seconds.