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.