The generator matrix

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

generates a code of length 8 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+18x^20+222x^24+6x^28+9x^32

The gray image is a linear code over GF(4) with n=32, k=4 and d=20.
This code was found by Heurico 1.16 in 0 seconds.