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

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+76x^35+85x^36+220x^37+291x^38+204x^39+55x^40+68x^41+12x^42+8x^43+3x^44+1x^70

The gray image is a linear code over GF(2) with n=304, k=10 and d=140.
This code was found by Heurico 1.16 in 0.031 seconds.