The generator matrix

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

generates a code of length 40 over Z4[X]/(X^3+2,2X) 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 20.1 seconds.