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  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  1  1  X  1  1
 0  X  0  0  0  0  X  X  X a*X  0  X a^2*X a*X a^2*X a*X  X  X a*X  0 a^2*X a*X  X a*X  0  X  0 a^2*X a*X  X a^2*X a*X  0 a*X a*X a^2*X  X a^2*X  0  X  X a^2*X  0  X  0 a*X a*X  X a^2*X a*X  X  0  0
 0  0  X  0  0  X a^2*X a*X a*X a*X  0  0 a*X a*X  0 a*X a^2*X a*X a^2*X a^2*X  0  X a^2*X  0 a^2*X  0 a*X a*X a*X a*X a^2*X  0 a^2*X  X  0 a*X  X  X a*X  0 a*X  0 a*X a^2*X  X  0 a*X a^2*X  X  0  X  0  X
 0  0  0  X  0 a^2*X  0  X a*X a^2*X  X  X  X  0  X a^2*X  X  X a^2*X a^2*X a^2*X a*X  0 a^2*X a^2*X  0  X a*X  0 a^2*X  0 a*X  X  0 a*X a^2*X  X  0 a*X a^2*X  0  X a*X a^2*X  0  0 a*X  X  0  X a*X a*X a^2*X
 0  0  0  0  X  X  X a^2*X  X  X  X a*X  0  0  0 a*X  X a*X a^2*X a^2*X a*X  0 a*X  X a*X a*X  0  0 a^2*X a^2*X a^2*X a*X  X a*X  0  X  X  X  0 a^2*X  X a*X a^2*X a*X a^2*X  0 a^2*X a^2*X  0  0 a^2*X a*X  0

generates a code of length 53 over F4[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+72x^144+165x^148+48x^150+192x^152+432x^154+144x^156+1296x^158+129x^160+1296x^162+66x^164+57x^168+66x^172+54x^176+21x^180+24x^184+18x^188+12x^192+3x^200

The gray image is a linear code over GF(4) with n=212, k=6 and d=144.
This code was found by Heurico 1.16 in 0.164 seconds.