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.