The generator matrix

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

generates a code of length 36 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+28x^35+87x^36+7x^40+4x^43+1x^44

The gray image is a linear code over GF(2) with n=288, k=7 and d=140.
This code was found by Heurico 1.16 in 0.015 seconds.