The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+130x^26+264x^27+282x^28+318x^29+250x^30+234x^31+205x^32+108x^33+126x^34+76x^35+22x^36+22x^37+6x^38+2x^39+2x^40

The gray image is a linear code over GF(2) with n=120, k=11 and d=52.
This code was found by Heurico 1.16 in 0.109 seconds.