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  1  2  2  1  1  1  2  1  1  2  1  1  1  1  1  2  2  1  1  1  1
 0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  0  8  8  0  8  8  0  8  8  8  8  0  0  0  8  8  0  8  0  8
 0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  0  0  0  8  8  0  8  8  0  0  0  0  0  8  8  0  8  8  0  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  8  8  0  8  8  8  0  8  8  0  0  8  8  0  8  8  8  0  0  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  0  0  0  0  0  8  8  0  8  8  0  0  8  0  8  8  0  8  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  8  0  8  8  8  0  0  8  8  8  0  0  8  8  0  8  8  8  8  0  8  8  8  8  8  8  8  0
 0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  0  8  8  0  8  8  0  8  0  0  8  0  8  0  0  8  8  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8  8  8  0  8  8  0  0  0  8  0  8  8  8  0  8  8
 0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  8  0  8  8  0  8  0  0  0  8  0  0  8  8  8  8  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+109x^36+8x^38+162x^40+120x^42+3319x^44+120x^46+145x^48+8x^50+73x^52+28x^56+2x^60+1x^76

The gray image is a code over GF(2) with n=352, k=12 and d=144.
This code was found by Heurico 1.16 in 0.674 seconds.