The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+28x^53+82x^54+6x^56+4x^58+4x^61+2x^62+1x^64

The gray image is a code over GF(2) with n=432, k=7 and d=212.
This code was found by Heurico 1.16 in 0.078 seconds.