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  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X X^3  X  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^2 X^2  0 X^2  0 X^3+X^2  0 X^2 X^2  0 X^3  0 X^3  0  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0 X^2 X^2  0 X^2 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3  0 X^3+X^2 X^3 X^3 X^3  0 X^3 X^3  0
 0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+43x^48+16x^49+203x^50+22x^51+164x^52+16x^53+20x^54+8x^55+16x^56+1x^66+2x^67

The gray image is a linear code over GF(2) with n=408, k=9 and d=192.
This code was found by Heurico 1.16 in 0.094 seconds.