The generator matrix

 1  0  1  1  1 2X X+2  1  1  1  1  2  1  1 3X+2  1  1  X  1  1 2X+2  1  1 3X  1  1  1  1  1  1  1  1  1 2X  X 3X  2  1 X+2 X+2
 0  1 X+1 3X+2  3  1  1  X X+1 X+2 X+3  1 2X 2X+3  1  2  1  1 2X+2 3X+3  1 3X 2X+1  1 2X  2 3X+2 2X  X  2 3X+2  X 3X+3  1 3X+2  1  X  1  1  1
 0  0  2 2X+2 2X  2  0  2 2X  0 2X+2 2X+2  2  2  2 2X+2 2X+2 2X+2  0 2X  0  0 2X  0 2X+2  2  2 2X 2X+2 2X  0 2X  0 2X 2X+2 2X  2  0 2X+2  2

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+294x^38+160x^39+230x^40+64x^41+184x^42+32x^43+55x^44+2x^46+1x^52+1x^56

The gray image is a code over GF(2) with n=320, k=10 and d=152.
This code was found by Heurico 1.16 in 19.8 seconds.