The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+290x^35+84x^36+408x^37+16x^38+108x^39+24x^40+88x^41+2x^43+3x^48

The gray image is a linear code over GF(2) with n=296, k=10 and d=140.
This code was found by Heurico 1.16 in 10.1 seconds.