The generator matrix

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

generates a code of length 5 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+15x^4+480x^6+90x^8+3840x^9+4320x^10+27150x^12+23040x^13+12960x^14+61440x^15+81045x^16+34560x^17+12960x^18+243x^20

The gray image is a linear code over GF(4) with n=20, k=9 and d=4.
This code was found by Heurico 1.16 in 0.942 seconds.