The generator matrix

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

generates a code of length 51 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+115x^44+112x^46+32x^47+273x^48+128x^49+272x^50+192x^51+320x^52+128x^53+208x^54+32x^55+143x^56+48x^58+25x^60+14x^64+3x^68+1x^72+1x^84

The gray image is a linear code over GF(2) with n=204, k=11 and d=88.
This code was found by Heurico 1.16 in 0.351 seconds.