The generator matrix

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

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+250x^36+756x^37+1224x^38+1416x^39+1368x^40+1232x^41+824x^42+536x^43+382x^44+124x^45+32x^46+32x^47+15x^48

The gray image is a code over GF(2) with n=320, k=13 and d=144.
This code was found by Heurico 1.16 in 0.359 seconds.