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

generates a code of length 40 over Z4[X]/(X^3+2,2X) 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 8.41 seconds.