The generator matrix

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

generates a code of length 9 over F4[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+108x^22+30x^24+216x^26+384x^27+18x^28+252x^30+9x^32+6x^36

The gray image is a linear code over GF(4) with n=36, k=5 and d=22.
This code was found by Heurico 1.16 in -6.87e-008 seconds.