The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X
0 X 0 X+2 0 X+2 0 X 2 X+2 2 X+2 2 X 2 X 0 X+2 0 X+2 0 2
0 0 2 0 0 2 2 2 2 0 2 2 0 2 0 0 0 0 0 2 2 2
0 0 0 2 2 2 2 0 0 0 2 0 2 2 0 2 0 0 2 2 0 0
generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+22x^20+84x^22+16x^24+4x^26+1x^40
The gray image is a code over GF(2) with n=88, k=7 and d=40.
This code was found by Heurico 1.16 in 0.00332 seconds.