The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+84x^40+38x^42+270x^44+254x^46+865x^48+3548x^50+6286x^52+3548x^54+845x^56+254x^58+269x^60+38x^62+58x^64+21x^68+3x^72+1x^76+1x^84

The gray image is a code over GF(2) with n=416, k=14 and d=160.
This code was found by Heurico 1.16 in 5.7 seconds.