The generator matrix

 1  0  1  1  1 3X+2  1  1 2X  1  1 X+2  1  2  1  1  X  1 2X+2 3X  1  1  1  1  1  1  0  0  X 3X+2  1 2X+2  1  1  1  1  1 2X  1  1
 0  1 X+1 3X+2 2X+3  1 2X+1 2X  1 3X+3 X+2  1 2X+2  1  3 3X  1 X+1  1  1  2 X+3  X  1  0  0  1  1 3X  1 2X+2  1 2X+2 3X  X 3X+1 3X 2X+2  X 2X+1
 0  0 2X+2  0 2X  0 2X 2X+2 2X+2  2  2  2 2X+2  0  2 2X 2X+2  0 2X+2 2X  0 2X 2X+2  2  0 2X+2  0 2X+2  2  0  2 2X 2X  2 2X 2X+2 2X+2 2X+2  0 2X+2
 0  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X 2X  0 2X  0  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+262x^37+321x^38+346x^39+294x^40+324x^41+230x^42+156x^43+47x^44+54x^45+1x^46+10x^47+1x^52+1x^56

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 8.34 seconds.