The generator matrix

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

generates a code of length 52 over F4[X]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+51x^140+108x^142+168x^143+444x^144+240x^146+732x^147+831x^148+456x^150+876x^151+1275x^152+528x^154+1416x^155+1761x^156+876x^158+1776x^159+1761x^160+672x^162+924x^163+744x^164+192x^166+252x^167+165x^168+39x^172+39x^176+15x^180+24x^184+9x^188+3x^192+6x^196

The gray image is a linear code over GF(4) with n=208, k=7 and d=140.
This code was found by Heurico 1.16 in 1.11 seconds.