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

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+51x^36+206x^37+291x^38+312x^39+454x^40+268x^41+220x^42+116x^43+41x^44+46x^45+17x^46+12x^47+12x^48+1x^64

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 0.078 seconds.