The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  0 X^2  0  1  0  1  1  X  0  1  1  1  X  1  1
 0  X  0  X  0  0  X X^2+X  0  0  X X^2+X  X X^2  X  0  X  X X^2  0 X^2  0  X  X X^2+X X^2  X X^2 X^2+X  X
 0  0  X  X  0 X^2+X  X  0  0 X^2+X  X X^2  X  X X^2  X  X  0  0  X X^2 X^2+X  X  0  X  X X^2  X  0  X
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0  0 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 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+52x^20+38x^21+138x^22+176x^23+290x^24+486x^25+798x^26+1232x^27+1694x^28+2140x^29+2230x^30+2160x^31+1727x^32+1292x^33+804x^34+496x^35+280x^36+126x^37+110x^38+32x^39+46x^40+14x^41+14x^42+6x^44+2x^46

The gray image is a linear code over GF(2) with n=120, k=14 and d=40.
This code was found by Heurico 1.16 in 5.56 seconds.