The generator matrix

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

generates a code of length 16 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+192x^40+96x^42+492x^44+576x^46+1065x^48+864x^50+756x^52+30x^56+24x^60

The gray image is a linear code over GF(4) with n=64, k=6 and d=40.
This code was found by Heurico 1.16 in 0.0187 seconds.