The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+32x^20+26x^21+92x^22+144x^23+267x^24+484x^25+605x^26+1660x^27+1316x^28+2800x^29+1582x^30+2796x^31+1189x^32+1684x^33+686x^34+500x^35+244x^36+118x^37+92x^38+20x^39+23x^40+8x^41+13x^42+2x^46

The gray image is a linear code over GF(2) with n=120, k=14 and d=40.
This code was found by Heurico 1.16 in 4 seconds.