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  2  1  1  1  2  1  2  1  1  1  1  1  1  1  4  4  1  1  1  1  2
 0 12  0 12  0 12  0  4  8 12  0 12 12  0  8  4  0  8 12  4 12  4  0 12  0  8  8  8 12 12 12 12  4  4 12  4  0 12  8 12  4  0  0  0
 0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  0  0  0  0  8  0  8  0  8  0  0  0  8  8  0  8  8  0  8  8  0  8  0  8  0  8  8  8  0
 0  0  0  8  0  0  0  8  0  0  0  8  0  0  0  8  8  8  0  8  8  0  0  0  8  8  0  8  0  8  8  8  0  0  0  8  8  8  8  8  8  8  8  8
 0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  8  0  8  0  0  0  0  0  8  0  8  8  8  8  0  8  0
 0  0  0  0  0  8  0  8  0  8  8  0  0  8  8  0  0  8  0  0  0  8  8  0  0  8  0  8  8  8  8  8  8  8  0  8  0  8  0  0  8  8  8  8
 0  0  0  0  0  0  8  0  8  0  8  0  0  0  8  0  0  0  8  8  8  8  8  8  8  8  8  8  8  0  0  8  8  0  0  0  0  0  0  0  8  8  0  0

generates a code of length 44 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+52x^38+90x^40+32x^41+152x^42+352x^43+727x^44+352x^45+146x^46+32x^47+49x^48+22x^50+24x^52+10x^54+4x^56+2x^58+1x^76

The gray image is a code over GF(2) with n=352, k=11 and d=152.
This code was found by Heurico 1.16 in 0.123 seconds.