The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+116x^37+287x^38+318x^39+584x^40+924x^41+1797x^42+2212x^43+3907x^44+2320x^45+1830x^46+836x^47+544x^48+316x^49+175x^50+84x^51+73x^52+36x^53+5x^54+6x^55+11x^56+1x^62+1x^70

The gray image is a code over GF(2) with n=352, k=14 and d=148.
This code was found by Heurico 1.16 in 30.7 seconds.