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 0 X^2 1 1 X 1 X^2 1 1 X 1 1 1 X 1 X^2 X 1 X 1 X^2 1 1 X^2 1 1 1 X 1
0 X 0 0 0 0 0 X^2 X^2 X X^2+X X X X X^2+X X 0 X^2+X X^2 X X^2 X X^2 0 X X^2+X X X^2+X X 0 X^2+X X X^2 0 0 X^2 0 X X^2 X^2 X X X^2 X^2 X^2 X 0 0 X X^2+X 0
0 0 X 0 0 X^2 X^2+X X X X X X X^2+X 0 0 0 X^2 X^2 X^2+X X X^2 0 X X X 0 X X^2 0 0 X X^2+X X^2+X X X^2 X^2 0 X^2 0 X^2 X 0 X 0 0 X^2 0 X X^2+X X^2 0
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 0 X X X^2 X X^2 X^2+X 0 X^2+X 0 0 X^2+X X X X^2 X X^2 0 X^2 X X^2 0 X^2 X^2+X X^2 0 X X^2 X X^2+X X^2+X X 0 X X^2 X^2 0 X 0
0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X^2 X X^2 X^2+X X X X^2 X^2 X^2+X 0 X^2+X 0 X^2 0 X X^2 X^2 X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 X^2 X X X X^2 X X^2+X 0 X X^2 X 0 0 X 0
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+47x^44+78x^45+108x^46+136x^47+168x^48+218x^49+219x^50+220x^51+212x^52+178x^53+126x^54+102x^55+57x^56+46x^57+45x^58+32x^59+19x^60+8x^61+11x^62+6x^63+8x^64+2x^66+1x^78
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 0.259 seconds.