The generator matrix

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

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+33x^24+72x^26+96x^27+165x^28+48x^30+288x^31+234x^32+72x^34+15x^36

The gray image is a linear code over GF(4) with n=40, k=5 and d=24.
This code was found by Heurico 1.16 in 6.87e-008 seconds.