The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+64x^21+375x^22+950x^23+2134x^24+3886x^25+6737x^26+10290x^27+14125x^28+17482x^29+18684x^30+17658x^31+14200x^32+10512x^33+6959x^34+3678x^35+1943x^36+876x^37+328x^38+128x^39+45x^40+10x^41+4x^42+2x^45+1x^46

The gray image is a linear code over GF(2) with n=120, k=17 and d=42.
This code was found by Heurico 1.13 in 65.9 seconds.