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

generates a code of length 40 over Z4[X]/(X^3+2,2X) 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 0.062 seconds.