The generator matrix

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

generates a code of length 7 over F4[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+15x^16+30x^20+192x^21+18x^28

The gray image is a linear code over GF(4) with n=28, k=4 and d=16.
This code was found by Heurico 1.16 in -3.62e-008 seconds.