The generator matrix

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

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+142x^37+447x^38+306x^39+476x^40+178x^41+272x^42+90x^43+65x^44+40x^45+17x^46+12x^47+1x^48+1x^60

The gray image is a code over GF(2) with n=320, k=11 and d=148.
This code was found by Heurico 1.16 in 0.062 seconds.