The generator matrix

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

generates a code of length 36 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+307x^30+1826x^31+4435x^32+8836x^33+16090x^34+21540x^35+24756x^36+21632x^37+16632x^38+9076x^39+3800x^40+1460x^41+502x^42+132x^43+28x^44+8x^45+5x^46+2x^47+4x^48

The gray image is a linear code over GF(2) with n=288, k=17 and d=120.
This code was found by Heurico 1.16 in 65.8 seconds.