The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X  X  0  X  X  1
 0  X  0 3X+2  0 X+2  0 3X  2 X+2 2X+2  X  2 3X+2 2X+2 3X 2X 2X X+2 2X  X 2X+2 3X  2 X+2 2X 2X 3X+2 3X 2X+2  2 3X+2  X X+2  X 3X+2  X  0  2  2
 0  0 2X+2  2 2X 2X+2  2 2X  2  0  0  2 2X+2 2X 2X 2X+2 2X+2 2X 2X  2 2X+2 2X+2  0  0  2  0 2X+2  0  2  2 2X 2X+2 2X  0 2X+2  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+64x^38+116x^39+155x^40+120x^41+31x^42+20x^43+4x^44+1x^66

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 0.046 seconds.