The generator matrix

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

generates a code of length 10 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+192x^21+1248x^22+1086x^24+1728x^25+3744x^26+3072x^27+6096x^28+5184x^29+13344x^30+9216x^31+9135x^32+5184x^33+6240x^34+48x^36+18x^40

The gray image is a linear code over GF(4) with n=40, k=8 and d=21.
This code was found by Heurico 1.16 in 0.896 seconds.