The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1  1 2X+2  1  X  1  1  0  1 2X+2
 0  2  0  0  0 2X+2  2 2X+2  0 2X  2  2  0 2X  2  2  0 2X  2  2 2X+2  2 2X+2 2X  0 2X 2X+2 2X+2  2 2X  0  0 2X 2X+2  2  0  2 2X+2  2 2X+2
 0  0  2  0 2X+2 2X+2 2X+2 2X  0 2X 2X+2  2 2X+2 2X+2 2X 2X  0  2  2  0  0 2X+2  0  0 2X+2  0  2 2X 2X+2  2 2X  0 2X+2  2 2X 2X  0 2X  0 2X+2
 0  0  0  2 2X+2 2X  2  2  0  2 2X  2 2X+2  0  2  0 2X  2 2X+2 2X+2  2  0  0  0 2X 2X+2 2X+2 2X 2X 2X+2  0 2X+2 2X  0 2X  0  2 2X  2  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X  0  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+199x^36+84x^37+704x^39+154x^40+648x^41+96x^43+112x^44+4x^45+45x^48+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 8.16 seconds.