The generator matrix

 1  0  1  1  1 X+2  1  X  1  2  1  1  1  1 2X  1  1 X+2  1  1 3X+2  1 2X+2  1  1  1 3X  0 3X+2  1  1 2X  1  0 2X+2  1  1  1  1  1
 0  1 X+1 3X+2  3  1  2  1 3X+3  1 X+2 2X+3  X 2X+1  1 3X+1  0  1 3X  1  1 2X  1 2X+3 X+1 X+3  1  1  1  1 2X+2  1 3X+2  1  1  3 2X+3 X+3  2 3X+2
 0  0 2X+2  0  2 2X+2  0 2X+2  2 2X 2X+2  0  2 2X  2  2 2X  2 2X 2X+2  0 2X+2 2X+2  0 2X 2X 2X 2X 2X 2X+2 2X+2  2 2X  2  2  0 2X  0  0  0
 0  0  0 2X  0  0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0  0  0 2X  0 2X 2X  0 2X 2X 2X
 0  0  0  0 2X  0 2X 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X  0  0  0  0 2X  0 2X

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

Homogenous weight enumerator: w(x)=1x^0+208x^36+224x^37+698x^38+544x^39+781x^40+544x^41+668x^42+224x^43+180x^44+10x^46+5x^48+8x^52+1x^56

The gray image is a code over GF(2) with n=320, k=12 and d=144.
This code was found by Heurico 1.16 in 0.172 seconds.