The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  8  2  0  2  1  1  1  1  1  1  8  2  1  0  1  1  1  2  2  8  2  2  1
 0  2  0  6  0  6  0  6 14  4 10  0  6  2 14  0  2 14  2 10 10 12  6  4  6  4  2  2  8  2 14  0 10 12  2  0 10  6  0
 0  0 12  0  0  0  4  0  4  0  4  8  8  4  4  4  8  8  4  4  8  4  0 12 12  4  0  4  8  0  0 12  4 12  0  0  4  0  0
 0  0  0 12  0  0  0  0  0  0  0  0  4  4  8  8  4  4 12 12  8  4 12 12  4  8  8  8  4 12 12  4 12  8  0  8  8  8  0
 0  0  0  0 12  0  4  4  4  8  8 12 12  8 12  0  8  4  8  4  4  8  0  0  0  8  0 12  0 12 12  4  4  0  4  4 12  0  0
 0  0  0  0  0 12  8  4 12  4  4  4  0 12  8 12  8 12  0  4  0  0 12  4  8  4 12 12  4  8  8 12  8  8  0  4  0  8  0

generates a code of length 39 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+56x^30+94x^31+235x^32+390x^33+631x^34+1390x^35+2214x^36+3672x^37+5161x^38+5308x^39+4874x^40+3732x^41+2293x^42+1292x^43+644x^44+376x^45+183x^46+102x^47+62x^48+22x^49+28x^50+6x^51+2x^52

The gray image is a code over GF(2) with n=312, k=15 and d=120.
This code was found by Heurico 1.16 in 10.8 seconds.