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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+109x^44+132x^46+96x^47+265x^48+384x^49+780x^50+576x^51+828x^52+384x^53+188x^54+96x^55+162x^56+52x^58+27x^60+12x^64+3x^68+1x^84

The gray image is a code over GF(2) with n=408, k=12 and d=176.
This code was found by Heurico 1.16 in 0.515 seconds.