The generator matrix
1 0 1 1 1 1 1 1 1 0
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a (a+1)X+a+1 1
0 0 (a+1)X 0 X X (a+1)X X (a+1)X X
0 0 0 X aX X aX (a+1)X (a+1)X 0
generates a code of length 10 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+315x^24+1500x^28+2205x^32+60x^36+15x^40
The gray image is a linear code over GF(4) with n=40, k=6 and d=24.
This code was found by Heurico 1.16 in 0.00712 seconds.