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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+40x^37+101x^38+170x^39+236x^40+322x^41+459x^42+668x^43+1432x^44+1996x^45+3522x^46+4944x^47+4892x^48+5024x^49+3574x^50+2068x^51+1387x^52+668x^53+441x^54+294x^55+212x^56+126x^57+79x^58+48x^59+27x^60+16x^61+16x^62+3x^64+1x^68+1x^76

The gray image is a code over GF(2) with n=384, k=15 and d=148.
This code was found by Heurico 1.16 in 18.1 seconds.