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.