The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+181x^36+96x^37+120x^38+352x^39+578x^40+288x^41+216x^42+32x^43+159x^44+16x^46+8x^48+1x^72

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 0.093 seconds.