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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+71x^42+96x^43+212x^44+314x^45+416x^46+570x^47+951x^48+1472x^49+2377x^50+3404x^51+4141x^52+4596x^53+4215x^54+3476x^55+2434x^56+1536x^57+892x^58+568x^59+379x^60+258x^61+190x^62+66x^63+58x^64+16x^65+26x^66+12x^67+11x^68+3x^70+4x^72+1x^74+1x^76+1x^82

The gray image is a code over GF(2) with n=424, k=15 and d=168.
This code was found by Heurico 1.16 in 20.9 seconds.