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

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

Homogenous weight enumerator: w(x)=1x^0+64x^27+129x^28+178x^29+268x^30+426x^31+771x^32+1380x^33+1771x^34+1416x^35+791x^36+414x^37+232x^38+122x^39+91x^40+72x^41+32x^42+20x^43+8x^44+4x^45+1x^48+1x^50

The gray image is a code over GF(2) with n=272, k=13 and d=108.
This code was found by Heurico 1.16 in 8.46 seconds.