The generator matrix

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

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+36x^38+54x^39+89x^40+30x^41+28x^42+10x^43+6x^44+2x^53

The gray image is a code over GF(2) with n=320, k=8 and d=152.
This code was found by Heurico 1.16 in 0.032 seconds.