The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+105x^36+4x^37+246x^38+36x^39+382x^40+292x^41+772x^42+1220x^43+2185x^44+1196x^45+694x^46+268x^47+415x^48+44x^49+178x^50+12x^51+89x^52+28x^54+18x^56+2x^58+5x^60

The gray image is a code over GF(2) with n=352, k=13 and d=144.
This code was found by Heurico 1.16 in 1.12 seconds.