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  2  2  2  4  4  1  2  2  2  2  4  2  2  4  2  1  1  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  4  8  4  4  8  0  4  4  4 12  0  0  0  8  4  4 12  8  4 12 12  0  4  0  8  0 12
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4  4 12  8  4  0  0  8  8 12  4 12 12 12 12 12  8 12  0  0  0  8 12  0  0  0  4  8
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  8  8  4  0  0  4  0 12  0 12  4  0  0  8  4  8  4  4  4 12  0  0  4 12 12 12  8 12
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  8  0  8  0  8  0  0  8  0  0  8  8  8  8  8  0  8  0  8  8  8  8
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  0  0  8  0  0  0  0  8  8  8  0  8  0  0  0  8  8  8  0  0  8  0  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  0  0  8  0  8  8  8  8  8  8  0  8  0  8  0  8  0  0  8  8  8  0  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  0  8  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  8  8  8  0  0  0  8  0  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+60x^35+116x^36+190x^37+279x^38+360x^39+435x^40+600x^41+2692x^42+812x^43+5285x^44+888x^45+2660x^46+620x^47+467x^48+308x^49+220x^50+184x^51+78x^52+58x^53+27x^54+12x^55+17x^56+4x^57+8x^58+1x^60+2x^62

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 4.45 seconds.