The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  2  1  1  1  1  1  1  1  1  2  1  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  0  0  0  0  0  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  8  8  0  0  8  0  0  8  0  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  0  8  0  8  0  8  0  8  0  8  0  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  0  0  8  0  0  8  0  0  8  8  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  8  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  8  0  8  8  0  0  8  0  8  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  8  0  0  0  8  8  0  0  0  0  8  8  0  8  8  0
 0  0  0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  8  0  0  0  8  8  8  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  0  0  8  0  8  0  8  8  8  8  0  0  8  8  0  0  0  0

generates a code of length 34 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+63x^20+34x^22+262x^24+137x^26+32x^27+395x^28+224x^29+292x^30+672x^31+563x^32+1120x^33+25133x^34+1120x^35+501x^36+672x^37+556x^38+224x^39+186x^40+32x^41+307x^42+65x^44+140x^46+12x^48+23x^50+2x^54

The gray image is a code over GF(2) with n=272, k=15 and d=80.
This code was found by Heurico 1.16 in 8.25 seconds.