The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1  2  1 3X+2  1  1  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  0 2X  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 X+3  1 2X+3  1  2 3X 2X+1  1  0 3X+2 2X 3X X+2  X  2 2X+2 X+1 2X+3 3X+1  3 2X+2 2X+2 X+3  0
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0

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

Homogenous weight enumerator: w(x)=1x^0+46x^37+354x^38+66x^39+105x^40+66x^41+325x^42+46x^43+5x^44+8x^46+1x^50+1x^60

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.