The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+49x^40+46x^42+22x^43+101x^44+110x^45+108x^46+260x^47+246x^48+916x^49+1511x^50+1488x^51+1500x^52+912x^53+250x^54+252x^55+93x^56+108x^57+84x^58+26x^59+45x^60+2x^61+37x^62+11x^64+7x^66+2x^68+4x^70+1x^78

The gray image is a code over GF(2) with n=408, k=13 and d=160.
This code was found by Heurico 1.16 in 1.39 seconds.