The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 0 X 1 X X X 0 X 1 1 1
0 X 0 0 0 0 0 0 0 X X^2+X X^2+X X X^2+X X X^2+X X X^2+X X^2+X X^2 X^2 X^2 X X^2+X X^2 X X X^2+X X 0
0 0 X 0 0 0 X X^2+X X 0 0 X^2 X X^2+X X^2+X X^2+X X^2 0 X 0 X X X X X X^2 X^2+X X^2+X 0 0
0 0 0 X 0 X X X^2+X 0 X X X^2 0 X^2 X X X X^2+X X X X X X^2+X X^2 0 0 0 X X X^2+X
0 0 0 0 X X 0 X^2+X X X^2 X^2+X X^2+X X^2 X X^2+X 0 0 X^2+X 0 0 X X^2 X 0 X^2 0 X^2 X^2+X 0 X
0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0
0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0
0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 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+50x^21+136x^22+224x^23+342x^24+532x^25+767x^26+1176x^27+1687x^28+2124x^29+2287x^30+2072x^31+1738x^32+1200x^33+816x^34+584x^35+300x^36+178x^37+80x^38+40x^39+22x^40+12x^41+9x^42+5x^44+1x^46+1x^48
The gray image is a linear code over GF(2) with n=120, k=14 and d=42.
This code was found by Heurico 1.16 in 6.03 seconds.