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

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

Homogenous weight enumerator: w(x)=1x^0+45x^40+24x^41+105x^42+126x^43+315x^44+202x^45+480x^46+454x^47+1411x^48+1288x^49+2843x^50+1872x^51+2721x^52+1368x^53+1382x^54+544x^55+495x^56+156x^57+237x^58+66x^59+113x^60+30x^61+56x^62+10x^63+16x^64+4x^65+13x^66+3x^68+2x^70+2x^74

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 5.38 seconds.