The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+136x^36+120x^37+592x^38+736x^39+1505x^40+2112x^41+3508x^42+4720x^43+5905x^44+4632x^45+3612x^46+2304x^47+1497x^48+592x^49+444x^50+112x^51+148x^52+32x^53+36x^54+21x^56+3x^60

The gray image is a code over GF(2) with n=352, k=15 and d=144.
This code was found by Heurico 1.16 in 11.8 seconds.