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

generates a code of length 40 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+66x^37+71x^38+162x^39+443x^40+150x^41+48x^42+70x^43+12x^44+1x^78

The gray image is a code over GF(2) with n=320, k=10 and d=148.
This code was found by Heurico 1.16 in 0.047 seconds.