The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^3+X  X  1 X^3+X  1 X^3+X^2+X  1 X^3+X^2+X  1  1 X^2  1 X^3  1  1  1 X^3+X^2 X^3  X X^3+X^2 X^2  X X^2  1  1  1
 0  1  0  0 X^2 X^3+1  1  1 X^2+1 X^3+1 X^3+X^2  1 X^3+X^2  1 X^3+X^2+X  1 X^3+X  1 X^3 X^3 X^3+X X^2  1 X^3+X^2+X+1  X X^2+X X^3  1  1  X  1  1  1 X^2+1 X^2  0
 0  0  1  0 X^2+1  1 X^2 X^2+1 X+1 X^2+X  1 X^2 X^2+X+1 X+1  0 X^3+X X^3+X^2+1  1 X^2+1 X^3+X X^3 X^2 X^3+X X^3  X X^2+X+1  1 X^3+X^2+X+1 X^2+X X^2+X  X X^3+X^2+X+1 X+1  1 X^3+X^2+X+1  0
 0  0  0  1  1 X^2 X^2+1 X^3+1 X+1 X^2+X X^3+1 X^2+X+1 X^3  0 X^3+1 X^3+X^2 X^3+X+1 X^3+X^2+X  X X^2  1 X^3+X+1 X+1 X^2+X X^2 X+1 X+1 X^2+X+1  1  1  X X^3+X^2+1 X^3  1 X^3+X+1 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+106x^30+896x^31+2269x^32+4576x^33+7852x^34+10724x^35+12475x^36+10984x^37+8136x^38+4456x^39+1995x^40+784x^41+174x^42+84x^43+9x^44+8x^45+2x^46+3x^48+2x^50

The gray image is a linear code over GF(2) with n=288, k=16 and d=120.
This code was found by Heurico 1.16 in 21.2 seconds.