The generator matrix

 1  0  1  1  1 14  1  1  8  1  1 14  1  1  0 14  1  1  1  4  1  1 12  1  1  2  1  1  0  1  1  4 12  1  1  1  1  8  6  1  1  2  1 14
 0  1 11  6  1  1  0  3  1  5  6  1 14  3  1  1  3  8  6  1  7  5  1 12 13  1  8 13  1  0 11  1  2 15 12 15  3  1  1  4  0  2  3  1
 0  0 12  0  0  0  0  4  0  8  4 12  4  4 12  4  0  4  8  4  0  8  4  0  0  8 12 12 12  4  8 12  4  0 12  8 12  4  0  8  4 12  8 12
 0  0  0 12  0  0  0  0  8  8  8  8  0  4 12 12  4 12  0 12  0 12 12  4  4  4  0  4  8  4 12  8  4  8  4 12  8 12 12  8  0 12  0  8
 0  0  0  0  4  4 12  4 12  0  4  8  8  8  0 12 12 12  8  4 12  4  8 12  8  0  8  4 12  8  8  0  8  4  8  4  4 12 12  4 12  4  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  8  8  0  8  8  8  0  8  8  0  0  8  0  8  8  8
 0  0  0  0  0  0  8  8  8  8  0  8  8  0  8  0  0  8  8  8  8  8  0  8  0  0  0  0  0  8  0  0  8  0  0  0  0  8  0  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+62x^35+130x^36+234x^37+585x^38+1062x^39+2152x^40+4156x^41+7537x^42+10932x^43+11949x^44+10722x^45+7603x^46+4340x^47+2150x^48+950x^49+488x^50+222x^51+117x^52+60x^53+40x^54+22x^55+13x^56+6x^57+2x^58+1x^66

The gray image is a code over GF(2) with n=352, k=16 and d=140.
This code was found by Heurico 1.16 in 31.1 seconds.