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

generates a code of length 53 over F4[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+33x^136+294x^140+378x^144+48x^147+459x^148+576x^151+456x^152+2592x^155+363x^156+5184x^159+387x^160+3888x^163+462x^164+414x^168+345x^172+213x^176+144x^180+93x^184+42x^188+9x^192+3x^196

The gray image is a linear code over GF(4) with n=212, k=7 and d=136.
This code was found by Heurico 1.16 in 2.26 seconds.