The generator matrix

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

generates a code of length 7 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+36x^18+48x^19+6x^20+108x^22+48x^23+9x^24

The gray image is a linear code over GF(4) with n=28, k=4 and d=18.
This code was found by Heurico 1.16 in 6.87e-008 seconds.