The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+65x^34+182x^35+202x^36+186x^37+171x^38+106x^39+69x^40+38x^41+3x^50+1x^54

The gray image is a linear code over GF(2) with n=296, k=10 and d=136.
This code was found by Heurico 1.16 in 0.266 seconds.