The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2 X+2  1  1  1  0  1  1 X+2  1 X^2+2  1  1  1 X^2+X  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1  3 X+2  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1  1  3 X+2 X+1  1  0  3  1 X^2+X+3  1 X^2+X X^2+2 X^2+1  1 X^2+2 X+2  0 X^2+X X+2
 0  0  2  0  0  0  0  0  2  2  0  2  2  2  0  2  2  0  0  0  0  0  2  0  2  0  2  2  2  2  2  2  0  0  0  0  2  0  0  2
 0  0  0  2  0  0  2  0  2  2  2  0  2  2  0  0  0  2  2  0  0  0  0  2  2  2  0  2  2  2  2  2  2  2  2  0  0  0  0  0
 0  0  0  0  2  0  2  2  0  0  2  0  0  2  2  0  2  2  2  2  0  2  0  2  0  2  2  2  0  2  0  0  0  2  0  2  0  0  0  0
 0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  2  0  2  2  0  2  2  2  0  0  2  0  2  2  0  0  0  0  0  0  2  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+257x^36+256x^37+384x^38+768x^39+780x^40+768x^41+384x^42+256x^43+230x^44+1x^48+9x^52+2x^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 25.9 seconds.