The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1 2X+2  1  1  1  1  1  1  X  0  1  1  X  1  X  1
 0  X  0 3X+2 2X X+2  0  X  2 3X+2 2X+2 3X 2X+2 3X+2 2X+2  X  X  X 2X 3X 3X 2X 2X+2 3X+2  0  X  0 3X 3X+2 3X  0  X 3X+2  2 X+2  X X+2 3X+2 X+2 2X
 0  0 2X+2  0 2X 2X+2 2X+2  2  2  2 2X  2  2  0  0 2X 2X  0  2  0  2  0 2X+2  0  2 2X  0 2X+2  2 2X  0 2X+2 2X+2 2X+2 2X 2X 2X+2 2X  0 2X
 0  0  0 2X+2 2X+2  2 2X+2 2X  0  0 2X+2 2X+2  2  0 2X 2X+2 2X 2X+2 2X 2X  0 2X+2 2X+2 2X  0 2X 2X  2 2X+2  2  2  0  0 2X+2 2X  0  2 2X  0  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+111x^36+124x^37+272x^38+312x^39+440x^40+368x^41+212x^42+72x^43+76x^44+20x^45+26x^46+11x^48+2x^54+1x^68

The gray image is a code over GF(2) with n=320, k=11 and d=144.
This code was found by Heurico 1.16 in 0.343 seconds.