The generator matrix

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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 143.

Homogenous weight enumerator: w(x)=1x^0+1188x^143+495x^144+2232x^147+972x^148+3060x^151+996x^152+2424x^155+657x^156+2100x^159+609x^160+1008x^163+333x^164+276x^167+24x^168+3x^172+3x^176+3x^180

The gray image is a linear code over GF(4) with n=204, k=7 and d=143.
This code was found by Heurico 1.16 in 32.6 seconds.