The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+174x^46+140x^47+772x^48+736x^49+1606x^50+1244x^51+2499x^52+1980x^53+2814x^54+1220x^55+1588x^56+600x^57+478x^58+180x^59+205x^60+44x^61+72x^62+18x^64+4x^66+4x^68+4x^70+1x^72

The gray image is a code over GF(2) with n=424, k=14 and d=184.
This code was found by Heurico 1.16 in 4.21 seconds.