The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  X  X  1  X  1  X  X  X  X X^2  X  X  X  2  X  X
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2  2  2  0 X^2 X^2+2  0 X^2+2 X^2+2 X^2 X^2+2 X^2  2 X^2  2 X^2+2  0 X^2+2  2  0  2 X^2  2
 0  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  2  0  0  0  2  2  0  0  0  0  2  0  0  0  2  2  2  0  0  2  2  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  0  2  0  0  2  2  0  2  2  2  0  0  2  0  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  2  0  2  2  0  0  0  2  0  0  2  0  2  2  2  2  2  0  2  0  0  2  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+34x^37+76x^38+128x^39+58x^40+146x^41+40x^42+2x^44+8x^45+12x^46+1x^48+2x^49+2x^52+2x^53

The gray image is a code over GF(2) with n=320, k=9 and d=148.
This code was found by Heurico 1.16 in 65.5 seconds.