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

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+55x^36+50x^38+192x^39+431x^40+192x^41+60x^42+24x^44+18x^46+1x^76

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.