The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  2  8  2  1  1  1  1 12  1  1  0  4  1  8  1  2  1  2  2  1  1  1  2  1  2  1
 0  2  0 14  4  6 12  2  0  6 14 12  8  2 10  6  2  4 14  2 10 14  8  6  4  2  2  0  2  2  2  2  6  6 14  2  4 10  8  4 12  8  8  0
 0  0 12  4  4  0  0  4  0  0  4  8  4 12  8  0  0  4  4  4  0 12 12  0  4  8 12  0  8 12  4 12  8  0  0  4  4  8  4  0 12  4  4  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  0  8  8  0  8  8  0  8  8  8  0  0  8  0  0  0  8  8  8  0  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  0  0  0  8  0  8  8  0  0  8  0  0  8  8  8  8  8  8  8  8  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  0  8  8  0  0  8  8  8  8  0  8  8  8  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  8  0  0  0  8  0  8  0  8  8  0  8  0  8  8  0  8  0  8  8  8  0  0  8  8  8  8  8
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  0  8  8  0  8  0  8  0  8  8  8  8
 0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  0  0  8  0  8  0  0  0  0  8  8  0  0  8  0  0  8  0  8  8  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+35x^34+64x^35+147x^36+252x^37+421x^38+592x^39+1029x^40+2214x^41+3687x^42+5016x^43+5830x^44+5072x^45+3568x^46+2344x^47+1059x^48+580x^49+437x^50+168x^51+107x^52+68x^53+33x^54+8x^55+15x^56+6x^57+9x^58+4x^60+2x^62

The gray image is a code over GF(2) with n=352, k=15 and d=136.
This code was found by Heurico 1.16 in 12.4 seconds.