The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 1 1 1 1 0 1 X 0 1 X^2 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X X X^2+X X^2+X X^2+X X X X X^2 X^2 X X^2+X 0 X^2 0
0 0 X 0 0 0 0 0 0 0 X X^2+X X 0 X X^2 X^2+X X^2+X X^2 0 X X X^2+X X^2+X X^2+X X X X X X^2
0 0 0 X 0 0 0 X X^2+X X X X 0 X X^2+X X^2 X^2+X X^2+X X X^2+X 0 X^2 X^2+X 0 X X^2 0 0 X^2+X X^2
0 0 0 0 X 0 X X X X^2 0 0 X^2 X X X X 0 X^2+X 0 X^2 0 X^2 X^2+X X^2 X X X^2 X^2+X X^2
0 0 0 0 0 X X X^2 X^2+X X^2+X 0 X X X 0 X^2 X X^2 0 0 X X^2+X 0 X^2+X 0 X^2 0 X^2+X X 0
0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 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+58x^21+126x^22+226x^23+292x^24+380x^25+657x^26+1048x^27+1662x^28+2362x^29+2700x^30+2390x^31+1721x^32+1078x^33+629x^34+394x^35+269x^36+212x^37+105x^38+32x^39+21x^40+6x^41+6x^42+6x^43+1x^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 6.13 seconds.