The generator matrix

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

generates a code of length 52 over F4[X]/(X^2) who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+684x^142+888x^143+789x^144+468x^145+2448x^146+1884x^147+1635x^148+852x^149+4548x^150+3144x^151+2550x^152+1176x^153+5652x^154+3876x^155+3135x^156+1668x^157+6252x^158+4452x^159+2892x^160+1296x^161+5424x^162+3024x^163+1665x^164+600x^165+2340x^166+972x^167+591x^168+84x^169+300x^170+192x^171+45x^172+6x^176+3x^184

The gray image is a linear code over GF(4) with n=208, k=8 and d=142.
This code was found by Heurico 1.16 in 123 seconds.