The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+156x^35+795x^36+1124x^37+2242x^38+2264x^39+3424x^40+2166x^41+2305x^42+942x^43+595x^44+216x^45+92x^46+28x^47+13x^48+14x^49+1x^50+2x^51+4x^52

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 1.55 seconds.