The generator matrix

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

generates a code of length 40 over Z2[X]/(X^4) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+46x^37+354x^38+66x^39+105x^40+66x^41+325x^42+46x^43+5x^44+8x^46+1x^50+1x^60

The gray image is a linear code over GF(2) with n=320, k=10 and d=148.
This code was found by Heurico 1.16 in 0.032 seconds.