The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+549x^34+2224x^35+5402x^36+9308x^37+15150x^38+20508x^39+23698x^40+21720x^41+15820x^42+9432x^43+4574x^44+1660x^45+788x^46+156x^47+49x^48+16x^49+11x^50+4x^52+2x^54

The gray image is a code over GF(2) with n=320, k=17 and d=136.
This code was found by Heurico 1.16 in 81.2 seconds.