The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^53+78x^54+13x^56+8x^57+2x^58+1x^60+1x^68

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 0.125 seconds.