The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  1
 0 2X+2  0  2  0  0  2 2X+2  0  0  2 2X+2  0  0  2 2X 2X+2 2X 2X 2X+2 2X  2 2X 2X+2 2X  2 2X 2X 2X+2  2 2X 2X 2X+2  2  2  2 2X+2  2  0 2X
 0  0 2X+2  2  0 2X+2  2  0 2X  2 2X+2 2X 2X  2 2X+2  2 2X  2 2X 2X+2  2 2X 2X 2X+2  2 2X  0 2X+2  2  0  0 2X+2  2  0  2 2X+2  0  0  0 2X
 0  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0 2X  0 2X

generates a code of length 40 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+90x^38+331x^40+84x^42+3x^44+2x^46+1x^68

The gray image is a code over GF(2) with n=320, k=9 and d=152.
This code was found by Heurico 1.16 in 0.078 seconds.