The generator matrix

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

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+327x^140+204x^141+216x^142+348x^143+2067x^144+708x^145+480x^146+1284x^147+3942x^148+1776x^149+1068x^150+2040x^151+6615x^152+2244x^153+1212x^154+3000x^155+7761x^156+3324x^157+1392x^158+2940x^159+7965x^160+2652x^161+1080x^162+2244x^163+4674x^164+1128x^165+588x^166+432x^167+1305x^168+252x^169+108x^170+63x^172+48x^176+24x^180+12x^184+9x^188+3x^192

The gray image is a linear code over GF(4) with n=208, k=8 and d=140.
This code was found by Heurico 1.16 in 14.6 seconds.