The generator matrix

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

generates a code of length 49 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+458x^44+908x^46+807x^48+804x^50+542x^52+356x^54+168x^56+44x^58+8x^60

The gray image is a linear code over GF(2) with n=196, k=12 and d=88.
This code was found by Heurico 1.16 in 25.1 seconds.