The generator matrix

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

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+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 8.3 seconds.