The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  1  6  1  1  2  1  6  1 12  1  1  1  8  1  1  1  1  1  2 12  2  1  2  1  1  6  8  1  1  1  1  1
 0  1 11  6  5  1 11  0  1  5  1  6 13  1  8  3  1 14  1 12  1  9 13  2  1  0  1  6 15  2 14  1  4  5  6  1  5  1  1  1 15  8  8  0
 0  0 12  0  0  0  0  4  4 12 12  0  8  4  4  0  4 12  8  8 12  0 12  0 12 12  8 12 12 12  0  4 12 12  4 12  8  0  4 12  8  8 12  0
 0  0  0 12  0  4  4  4 12 12  8  0  4 12  8  8  0  0  0  8 12  8  0  4  0 12  4 12 12  0 12 12  0 12 12  8 12  8  0  8  0  4  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  0  8  0  8  8  8  8  0  8  8  8  0  8  0  0  0  0  0  8  8  0  0  8  8  8  8  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  0  0  8  8  8  0  0  8  8  8  8  8  0  0  8  0  8  8  0  8  0  8  8  0  8  0  0  0  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  0  0  0  8  0  8  0  8  0  8  0  0  0  8  8  8  8  8  8  8  0  8  0  0  8  8  0  0  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0  0  0  8  0  0  0  8  8  8  0  0

generates a code of length 44 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+27x^34+62x^35+169x^36+372x^37+484x^38+1072x^39+2250x^40+4446x^41+7624x^42+10440x^43+11682x^44+10392x^45+7615x^46+4508x^47+2271x^48+1100x^49+445x^50+282x^51+123x^52+68x^53+52x^54+20x^55+14x^56+6x^57+8x^58+2x^60+1x^62

The gray image is a code over GF(2) with n=352, k=16 and d=136.
This code was found by Heurico 1.16 in 29.6 seconds.