The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+162x^28+338x^29+616x^30+672x^31+933x^32+894x^33+985x^34+1014x^35+899x^36+560x^37+562x^38+324x^39+140x^40+30x^41+45x^42+6x^43+9x^44+2x^45

The gray image is a linear code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.16 in 1.16 seconds.