The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  X  X  0
 0  1  1  a (a+1)X+a+1  0 (a+1)X+1  a  X (a+1)X+a+1 aX+1 X+a X+a+1  X  1  1
 0  0 (a+1)X  X aX  X  0 (a+1)X aX (a+1)X aX  0  X  X  0 aX

generates a code of length 16 over F4[X,sigma]/(X^2) who�s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+369x^44+279x^48+372x^52+3x^60

The gray image is a linear code over GF(4) with n=64, k=5 and d=44.
This code was found by Heurico 1.16 in 0.016 seconds.