The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  1  X  X X^2+X  1  X  X X^2+X  1  X  0  1  1  1 X^2  1  1  1  0  X  0 X^2  1  1 X^2 X^2 X^2+X  1 X^2+X  1  1  1  1  0  1  1  1  1  1  1
 0  1  0  0  1  X  1  1 X^2 X^2+1  0 X+1  1 X^2+X  1  X  1  1  0 X^2+X+1  1  X X^2+1  0 X+1  1  X X^2+1 X^2+1  1  1  X  1 X^2+X X^2+X+1 X^2  1  1  1  1 X^2+X+1 X^2+X X+1 X^2+X+1  1 X^2+X  1  0 X^2+1  1  0
 0  0  1  0  X  1 X+1  1 X^2+1 X^2 X^2+X X+1  X  1  1 X^2+X X+1 X^2+1 X^2 X^2+X+1  0  1  0 X^2+1 X^2+1 X^2+X X^2 X^2+X  1 X+1  X  X  0 X^2+1 X^2+1  1 X^2+X+1  0  0 X^2+X+1  0  X X^2+X X^2+X+1 X^2 X+1 X^2  X X^2+X X^2+1  0
 0  0  0  1  X X^2+X X^2  1  1 X+1 X+1 X^2+1 X+1 X^2+X+1 X^2+X X+1  1 X^2  1 X^2  1  0 X^2+1  1 X^2+X+1 X^2+X X^2  X  1 X^2+1 X^2+1  1 X^2+X  0 X^2+X X+1  0  0  X X+1 X^2+X X^2+1 X^2 X+1 X+1 X^2+1 X^2+1  0  0  0  1
 0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 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+71x^44+290x^45+456x^46+690x^47+699x^48+828x^49+778x^50+860x^51+691x^52+768x^53+596x^54+592x^55+367x^56+206x^57+130x^58+94x^59+42x^60+18x^61+8x^62+2x^63+1x^64+2x^65+2x^67

The gray image is a linear code over GF(2) with n=204, k=13 and d=88.
This code was found by Heurico 1.11 in 0.766 seconds.