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  2  1  1  1  1  1  1  1  X  X  X
 0 2X+2  0 2X+2  0 2X+2 2X  2  0 2X+2  0 2X+2  2  0 2X 2X+2 2X 2X+2  2  0  0 2X 2X+2  2  0  0 2X 2X 2X+2 2X 2X+2  2  2  0 2X+2  0 2X 2X+2 2X+2 2X+2
 0  0 2X  0  0  0 2X  0  0  0  0 2X 2X  0  0 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0  0  0 2X 2X
 0  0  0 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X  0
 0  0  0  0 2X  0 2X  0  0 2X 2X  0 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X  0  0 2X  0 2X
 0  0  0  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0 2X  0 2X  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X  0 2X  0 2X  0  0  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+69x^36+104x^38+626x^40+128x^41+32x^42+39x^44+24x^46+1x^72

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 0.062 seconds.