The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+81x^26+144x^27+216x^28+232x^29+325x^30+702x^31+1582x^32+3000x^33+3758x^34+3062x^35+1625x^36+700x^37+349x^38+222x^39+169x^40+96x^41+53x^42+26x^43+23x^44+4x^45+9x^46+4x^47+1x^54

The gray image is a code over GF(2) with n=272, k=14 and d=104.
This code was found by Heurico 1.16 in 3 seconds.