The generator matrix

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

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+213x^36+128x^37+144x^38+22x^40+3x^44+1x^56

The gray image is a linear code over GF(2) with n=296, k=9 and d=144.
This code was found by Heurico 1.16 in 13 seconds.