The generator matrix

 1  0  1  1  1  1  1
 0  1 a^2*X+1  a a^2*X+a^2  X a*X+1

generates a code of length 7 over F4[X]/(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 -1.01e-007 seconds.