The generator matrix

 1  0  1  1  1 X^2+X  1  1  1 X^2+2  1 X+2  1  1  1  0  1 X^2+X  1  1  1  1  0  1 X^2+X  1 X^2+2 X+2  1  1  1  1 X^2+2  1  1 X+2  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3  3 X^2+2  1 X+2  1 X^2+1 X+1  0  1 X^2+X  1 X^2+X+3  3 X^2+X+3 X^2+2  1 X^2+X  1 X+2  1  1  0 X^2+1 X^2+2 X^2+1  1 X^2+3 X+2  1  3 X+1 X^2+X X^2+X+2
 0  0  2  0  0  0  2  0  2  2  2  2  2  0  0  0  0  0  2  2  0  2  2  2  2  0  0  0  0  2  0  2  0  0  2  2  2  0  0  2
 0  0  0  2  0  2  2  2  2  2  0  0  0  0  2  2  0  0  0  2  2  0  0  2  2  0  0  2  2  2  0  0  2  0  0  2  0  2  0  0
 0  0  0  0  2  0  2  2  0  0  0  0  2  2  0  0  0  0  2  2  2  0  0  0  0  2  2  2  2  0  2  0  2  0  2  2  0  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+50x^36+224x^37+154x^38+544x^39+107x^40+544x^41+148x^42+224x^43+44x^44+2x^46+3x^48+2x^52+1x^56

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 0.047 seconds.