The generator matrix

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

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+135x^24+144x^25+312x^26+192x^27+444x^28+288x^29+528x^30+576x^31+813x^32+336x^33+312x^34+12x^36+3x^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 -1.01e-007 seconds.