The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  0  X  X  1  1
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X+2 X^2+2 X^2+X  2 X^2+X+2  0 X^2+X X^2+2  X X^2+X+2  X  0 X+2  2 X^2  X  2  0 X+2 X^2+X  X  X X^2+X X^2 X^2 X^2  X X^2  X  0 X^2+2
 0  0 X^2+2  0 X^2 X^2  2 X^2  0  2  0  0 X^2 X^2 X^2+2 X^2 X^2 X^2+2 X^2+2 X^2+2  2  2 X^2+2 X^2+2 X^2 X^2+2 X^2+2 X^2+2 X^2+2  2 X^2+2  2  0 X^2 X^2+2  0 X^2+2 X^2  0  0
 0  0  0  2  0  0  2  0  0  0  2  2  2  2  2  2  0  0  2  2  2  2  0  2  2  2  0  2  0  2  0  2  0  2  0  2  2  0  2  0
 0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  0  0  0  0  2  2  0  2  0  0  2  2  0  2  2  2  0  2  2  2  0  2  0  2  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+142x^36+56x^37+192x^38+480x^39+388x^40+432x^41+180x^42+32x^43+72x^44+24x^45+40x^46+3x^48+4x^50+1x^52+1x^68

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 0.11 seconds.