The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  X  1 X^2+2  1 X^2+X  1 X^2+X+2  1  1  1  1 X^2+2  1  2  X  2 X^2+X+2  1  1  0  1  1  1  1  1  1  1  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+2 X+3  1 X^2+1  1 X^2+X+2  1 X^2+2  1 X^2+X+3 X^2+1 X^2  3  1 X^2+X+1  1  1  X  1 X+3 X+1  1 X^2+X+1 X+2 X+2 X^2+X+3  2 X^2+1 X^2+X X^2+X  0
 0  0  X  0 X+2  X X+2  2  0 X^2+X+2 X^2  X X^2 X^2 X+2 X^2+X+2 X^2+X X^2+2  2  2 X^2 X^2+X+2 X^2+X+2  X X^2 X^2 X+2  0  0 X^2+X+2 X+2 X^2 X+2  2 X^2+X+2  0 X^2+X X^2+2 X^2  2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  0  2  2  0  0  2  0  2  0  0  0  2  0  2  0  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 36.

Homogenous weight enumerator: w(x)=1x^0+80x^36+474x^37+520x^38+724x^39+647x^40+692x^41+439x^42+332x^43+71x^44+62x^45+27x^46+16x^47+4x^49+5x^50+1x^52+1x^54

The gray image is a code over GF(2) with n=320, k=12 and d=144.
This code was found by Heurico 1.16 in 0.157 seconds.