The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+19x^36+104x^37+28x^38+336x^39+35x^40+400x^41+27x^42+16x^43+9x^44+40x^45+8x^46+1x^74

The gray image is a code over GF(2) with n=320, k=10 and d=144.
This code was found by Heurico 1.16 in 0.047 seconds.