The generator matrix
1 0 0 1 1 1 X^2+X 1 1 1 X X^2+X 1 0 0 1 X^2 1 1 X 1 X^2+X X^2 1 1 1 X X 1 1
0 1 0 1 0 1 1 X 1 X 1 1 X+1 X 1 0 1 X^2+X X^2+1 1 X+1 X 1 X^2+X+1 0 X^2 1 1 X+1 0
0 0 1 1 1 0 1 X+1 1 X X^2+X X^2+1 X 1 0 X^2+X+1 X^2+X+1 X^2 X^2+X 0 1 1 X^2+1 X X+1 X^2+1 X^2+1 0 X 0
0 0 0 X 0 0 0 0 0 0 0 X^2 X^2 X X X X^2+X X^2 X^2 X^2+X X^2+X X X X 0 X X X X 0
0 0 0 0 X 0 0 0 X^2 X X X^2+X X^2+X X^2+X X 0 X^2 X X^2 0 X X^2+X X X^2 0 0 X^2 X X^2 0
0 0 0 0 0 X X^2+X X^2+X 0 X X^2+X 0 X^2 X^2+X X^2+X X X^2+X X X 0 X^2+X X X^2 X X X^2+X X^2 0 X^2 X^2
generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+71x^22+192x^23+540x^24+866x^25+1662x^26+2190x^27+4130x^28+3914x^29+5654x^30+3902x^31+4057x^32+2278x^33+1746x^34+794x^35+478x^36+174x^37+82x^38+26x^39+10x^40+1x^54
The gray image is a linear code over GF(2) with n=120, k=15 and d=44.
This code was found by Heurico 1.16 in 14.7 seconds.