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.