The generator matrix

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

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+363x^36+128x^37+706x^38+384x^39+1125x^40+384x^41+476x^42+128x^43+268x^44+98x^46+34x^48+1x^60

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 62.2 seconds.