The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  X  X  1  1  0  1  0  X  1  1  0  1  X  1  X
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  X  0 X^2+X X^2+X X^2+X  0  X  0  X X^2+X X^2+X  0  X X^2 X^2+X X^2+X  0
 0  0 X^2  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0  0 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 X^2 X^2  0 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+62x^22+168x^24+32x^25+262x^26+160x^27+650x^28+320x^29+820x^30+320x^31+579x^32+160x^33+340x^34+32x^35+116x^36+46x^38+20x^40+6x^42+2x^44

The gray image is a linear code over GF(2) with n=120, k=12 and d=44.
This code was found by Heurico 1.16 in 0.474 seconds.