The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+152x^35+848x^36+1446x^37+1857x^38+2336x^39+3180x^40+2458x^41+1906x^42+1124x^43+702x^44+242x^45+69x^46+36x^47+11x^48+12x^49+2x^52+2x^57

The gray image is a code over GF(2) with n=320, k=14 and d=140.
This code was found by Heurico 1.16 in 1.53 seconds.