The generator matrix

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

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+137x^36+428x^37+494x^38+776x^39+454x^40+832x^41+448x^42+376x^43+82x^44+20x^45+30x^46+9x^48+4x^50+5x^52

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 0.156 seconds.