The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+114x^35+195x^36+344x^37+575x^38+448x^39+825x^40+474x^41+517x^42+286x^43+145x^44+100x^45+19x^46+12x^47+18x^48+10x^49+7x^50+4x^51+2x^54

The gray image is a code over GF(2) with n=320, k=12 and d=140.
This code was found by Heurico 1.16 in 56.7 seconds.