The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+70x^26+234x^27+640x^28+1122x^29+1948x^30+2424x^31+3687x^32+3788x^33+4570x^34+4100x^35+3993x^36+2450x^37+1824x^38+962x^39+559x^40+248x^41+100x^42+22x^43+15x^44+8x^45+2x^47+1x^48

The gray image is a linear code over GF(2) with n=136, k=15 and d=52.
This code was found by Heurico 1.16 in 16.2 seconds.