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

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

Homogenous weight enumerator: w(x)=1x^0+43x^36+142x^38+128x^39+436x^40+128x^41+94x^42+25x^44+18x^46+6x^48+2x^50+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 0.047 seconds.