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

generates a code of length 40 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+68x^37+83x^38+248x^39+293x^40+196x^41+57x^42+36x^43+10x^44+24x^45+3x^46+4x^47+1x^74

The gray image is a code over GF(2) with n=320, k=10 and d=148.
This code was found by Heurico 1.16 in 8.14 seconds.