The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+60x^27+148x^28+136x^29+126x^30+146x^31+127x^32+112x^33+54x^34+42x^35+44x^36+8x^37+10x^38+6x^39+2x^42+2x^43

The gray image is a linear code over GF(2) with n=124, k=10 and d=54.
This code was found by Heurico 1.16 in 0.0323 seconds.