The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^51+2x^52+12x^53+4x^54+2x^55+1x^56

The gray image is a linear code over GF(2) with n=408, k=6 and d=204.
This code was found by Heurico 1.16 in 0.063 seconds.