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  1  X  1  1  1  0  X  1  1  1  1  1  1  1  1  0  1
 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 a*X+1 a^2*X+a X+a^2  a  X X+a^2  a a^2*X+a  1  1 a*X+1 a^2*X  a X+a^2 a*X  X a*X a^2*X  1 X+a
 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^2*X+a^2 X+a a*X+1 a^2*X+a X+a  1 X+a^2 X+a^2 a^2*X+a^2 a*X X+a  0 X+1 a*X+a a*X+1 a*X+a  X a*X+a a^2*X+1 a^2*X+a^2  0
 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 a*X a*X  0  X  0 a*X a*X  0 a^2*X a^2*X  0  0 a*X a*X  X a^2*X a^2*X a*X  0  X a*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+1236x^143+519x^144+2304x^147+855x^148+2808x^151+1026x^152+2580x^155+756x^156+1992x^159+657x^160+1116x^163+258x^164+252x^167+18x^168+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 838 seconds.