The generator matrix

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

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+56x^35+96x^36+138x^37+224x^38+332x^39+380x^40+340x^41+224x^42+104x^43+96x^44+28x^45+12x^47+2x^48+4x^49+8x^51+2x^53+1x^64

The gray image is a code over GF(2) with n=320, k=11 and d=140.
This code was found by Heurico 1.16 in 138 seconds.