The generator matrix

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

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+208x^36+224x^37+698x^38+544x^39+781x^40+544x^41+668x^42+224x^43+180x^44+10x^46+5x^48+8x^52+1x^56

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 0.172 seconds.