The generator matrix

 1  0  1  1  2  1  1  1 X+2  1  1  X  1  0  1 3X 3X  1  1  1 X+2  1  2  1  2  1  1  1  1  1  1 3X+2  1  1  1 3X+2  X  1  1  1
 0  1  1 X+2  1 X+3  2  3  1 3X 3X+1  1  3  1 3X+2  1  1 2X+2 X+1 2X+1  1 X+3  1 2X+1  1 X+1 3X+2  1 X+1 X+2 2X+1  1  2 3X+1 2X+1  1  0 3X+1 3X 2X
 0  0  X  0 3X  X 3X 2X  0 3X+2 2X+2  X 2X+2 2X+2 3X  2 X+2 X+2 2X 2X 2X+2 X+2 2X+2 3X+2  X  X  2  2  0 3X+2 3X+2 X+2 2X+2 3X+2 3X  0 X+2 3X+2 2X 2X+2
 0  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  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+90x^36+328x^37+815x^38+556x^39+733x^40+472x^41+624x^42+256x^43+142x^44+32x^45+12x^46+20x^47+9x^48+4x^50+1x^54+1x^56

The gray image is a code over GF(2) with n=320, k=12 and d=144.
This code was found by Heurico 1.16 in 0.141 seconds.