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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+50x^35+120x^36+200x^37+226x^38+312x^39+383x^40+828x^41+1731x^42+2674x^43+3327x^44+2762x^45+1661x^46+850x^47+420x^48+302x^49+183x^50+124x^51+92x^52+62x^53+37x^54+22x^55+8x^56+6x^57+2x^58+1x^68

The gray image is a code over GF(2) with n=352, k=14 and d=140.
This code was found by Heurico 1.16 in 4.33 seconds.