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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+58x^36+84x^37+154x^38+220x^39+458x^40+468x^41+844x^42+1312x^43+1078x^44+1298x^45+888x^46+424x^47+391x^48+162x^49+136x^50+80x^51+56x^52+34x^53+22x^54+12x^55+6x^56+2x^57+4x^58

The gray image is a code over GF(2) with n=352, k=13 and d=144.
This code was found by Heurico 1.16 in 1.06 seconds.