The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+79x^36+108x^37+38x^38+22x^39+2x^40+4x^41+2x^43

The gray image is a linear code over GF(2) with n=296, k=8 and d=144.
This code was found by Heurico 1.16 in 0.016 seconds.