The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  0  X  X  1  1
 0  X  0 3X+2 2X+2 X+2  2  X  0 3X  2 3X+2 2X X+2  0 3X+2  2  X X+2  X  0 3X 2X 2X+2  X 2X  0 3X 3X+2  X  X 3X+2 2X+2 2X+2 2X+2  X 2X+2  X  0  2
 0  0  2  0 2X+2 2X+2 2X 2X+2  0 2X  0  0 2X+2 2X+2  2 2X+2 2X+2  2  2  2 2X 2X  2  2 2X+2  2  2  2  2 2X  2 2X  0 2X+2  2  0  2 2X+2  0  0
 0  0  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0
 0  0  0  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0 2X  0  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X 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+142x^36+56x^37+192x^38+480x^39+388x^40+432x^41+180x^42+32x^43+72x^44+24x^45+40x^46+3x^48+4x^50+1x^52+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 0.109 seconds.