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

generates a code of length 40 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+19x^36+104x^37+28x^38+336x^39+35x^40+400x^41+27x^42+16x^43+9x^44+40x^45+8x^46+1x^74

The gray image is a linear code over GF(2) with n=320, k=10 and d=144.
This code was found by Heurico 1.16 in 0.047 seconds.