The generator matrix

 1  0  0  1  1  1 2X+2  0 2X 2X+2  1  1  1  1 X+2  1  1 X+2  1  1 X+2  1  1  1  X  1  1  X  1  1  1 3X  1  1 3X 2X  1 X+2  2  1
 0  1  0  0  3  3  1 3X+2  1  1 2X 2X+3  2  1 3X 3X 3X+1  1 3X+1 X+2  1 X+1  1  2  1  2 2X+1  1 X+3 X+3 X+1 X+2 X+2 3X+3  1  1 3X  0 3X+2 2X+2
 0  0  1 X+1 3X+3 2X+2 3X+3  1 X+2  1 X+2 2X+1 2X+3 3X  1 2X+3 3X+2 2X+1 X+3  2 X+2  2 X+1 3X+1 3X+3  1  0 3X+1  1  3 3X  1 2X+3 2X+2 X+2 3X  3  1  1 2X+2
 0  0  0 2X 2X  0 2X 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X 2X  0  0  0  0  0 2X 2X 2X  0 2X 2X 2X  0 2X 2X  0  0  0  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+220x^36+766x^37+1244x^38+1368x^39+1557x^40+1072x^41+903x^42+476x^43+296x^44+198x^45+60x^46+20x^47+6x^48+4x^49+1x^50

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 0.406 seconds.