The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+80x^39+134x^40+172x^41+267x^42+358x^43+601x^44+1010x^45+1703x^46+2496x^47+2800x^48+2484x^49+1731x^50+996x^51+569x^52+344x^53+235x^54+144x^55+98x^56+80x^57+30x^58+22x^59+18x^60+6x^61+2x^62+2x^64+1x^72

The gray image is a code over GF(2) with n=384, k=14 and d=156.
This code was found by Heurico 1.16 in 6.11 seconds.