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  1  1  1  1  1  1  1 X^2  1  1  1  1  1  0  1  1 X^2  X
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X+2 X^2+2 X^2+X X^2 X^2+X X+2  0 X^2+X+2  2  X X^2+2  0  2 X^2+X X^2+X+2 X+2 X+2 X^2+2 X^2  2 X^2+2 X^2+X  0  0 X^2+X X^2+X+2  X X^2+2 X+2 X^2+2 X^2+X
 0  0  2  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  2  0  2  2  2  0  0  2  2  0  2  2  2  0  2  0  0  0  2  2
 0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  0  0  2  0  2  2  0  0  2  2  2
 0  0  0  0  2  0  0  2  2  2  0  2  0  0  2  2  0  0  2  2  2  2  0  2  2  0  0  2  2  0  0  0  0  2  2  0  0  2  0  0
 0  0  0  0  0  2  2  2  2  0  0  0  2  0  0  2  2  2  2  0  2  2  2  0  2  2  0  0  0  0  0  2  0  2  0  0  0  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+181x^36+96x^37+120x^38+352x^39+578x^40+288x^41+216x^42+32x^43+159x^44+16x^46+8x^48+1x^72

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 0.094 seconds.