The generator matrix

 1  0  0  1  1  1  2  0 X^2  1  1  1  1  2 X+2 X^2  1  1  1  X  1 X^2+X  1 X^2+2  X  1  1 X^2+X+2  1  1  1  1  X  1 X+2  0 X^2+X  1  1  1
 0  1  0  0 X^2+3 X^2+3  1 X^2+X  1 X^2  3  2 X^2+1  1 X^2+X  1 X+1 X^2+X+2 X+1  1  X  1 X^2+X+2  1  1 X^2+2 X^2+1 X^2+X+2  2 X^2+X+3  1 X^2+2  1 X+3  2 X+2  1  3  X  2
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X  X X^2+X X^2+3  3  1  1 X^2+X+2  2 X^2+2 X+3 X+3  1  0 X+1  0  1 X^2+X+3 X+1  1  1 X^2+X+2 X^2+3 X^2+X X^2+X+2 X^2+3  1  1 X^2+3 X+2 X^2+X  0
 0  0  0  2  2  0  2  2  2  2  2  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  0  2  2  0  2  0  2  0  2  0  0  0  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+210x^36+902x^37+1121x^38+1400x^39+1259x^40+1368x^41+778x^42+684x^43+252x^44+106x^45+85x^46+12x^47+6x^48+8x^49

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 0.375 seconds.