The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2) 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 25.6 seconds.