The generator matrix

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

generates a code of length 36 over Z2[X]/(X^4) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+194x^29+1105x^30+3290x^31+8397x^32+16816x^33+32312x^34+42588x^35+51539x^36+44286x^37+32519x^38+16574x^39+8076x^40+2918x^41+1122x^42+280x^43+83x^44+24x^45+14x^46+4x^47+2x^49

The gray image is a linear code over GF(2) with n=288, k=18 and d=116.
This code was found by Heurico 1.16 in 248 seconds.