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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+115x^40+70x^42+8x^43+387x^44+64x^45+382x^46+224x^47+1433x^48+1472x^49+2700x^50+2608x^51+2881x^52+1472x^53+1260x^54+224x^55+569x^56+64x^57+174x^58+8x^59+173x^60+22x^62+54x^64+15x^68+4x^72

The gray image is a code over GF(2) with n=408, k=14 and d=160.
This code was found by Heurico 1.16 in 5.66 seconds.