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 X^2  X  1 X^2+2  1  1  X  X  1  1
 0  X  0  X  2  0 X^2+X X^2+X X^2 X^2 X^2+X+2  X X+2 X^2+2 X^2 X^2+X X^2+X  X  2  2 X^2+X+2  2  X X^2  X X^2 X+2 X^2  0  0  X  X X^2+X+2  0  X X^2+2  X X+2 X^2+X+2  2
 0  0  X  X X^2 X^2+X X^2+X  0 X^2+2  X X^2 X^2+X+2 X^2  2 X^2+X X+2 X^2+X  X X^2 X^2+X+2 X^2+2  2 X+2 X+2 X^2 X^2+X+2  0  2 X+2  X X^2+2 X^2+2  X  X  0 X+2  0 X^2+X X+2 X^2+2
 0  0  0  2  2  2  0  2  0  0  2  2  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  2  2  0  2

generates a code of length 40 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+73x^36+162x^37+337x^38+228x^39+525x^40+272x^41+238x^42+64x^43+63x^44+26x^45+41x^46+12x^47+1x^48+4x^49+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.