The generator matrix

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

generates a code of length 10 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+480x^22+318x^24+1440x^26+1488x^28+7968x^30+2223x^32+2400x^34+48x^36+18x^40

The gray image is a linear code over GF(4) with n=40, k=7 and d=22.
This code was found by Heurico 1.16 in 99.6 seconds.