The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  2  1  a a+1  3 3a+2 3a+1  2 3a 2a+1 2a+2
 0  0  1  0 2a+3  1 3a+3  a a+1 a+2 2a 3a 2a+3 2a+2 2a
 0  0  0  1 3a+3  2  1  a a+2 a+1 2a+3 3a+2  3 a+1 2a+1

generates a code of length 15 over GR(16,4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+120x^34+348x^35+222x^36+780x^37+1932x^38+1620x^39+1935x^40+2556x^41+4908x^42+5436x^43+5523x^44+6372x^45+10788x^46+8220x^47+5571x^48+4116x^49+3756x^50+1272x^51+36x^52+21x^56+3x^60

The gray image is a code over GF(4) with n=60, k=8 and d=34.
This code was found by Heurico 1.16 in 2.67 seconds.