The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^35+141x^36+234x^37+370x^38+798x^39+1158x^40+2548x^41+2578x^42+6610x^43+3760x^44+6668x^45+2697x^46+2558x^47+1090x^48+728x^49+337x^50+202x^51+102x^52+58x^53+33x^54+28x^55+19x^56+4x^57+1x^58+1x^60

The gray image is a code over GF(2) with n=352, k=15 and d=140.
This code was found by Heurico 1.16 in 13.2 seconds.