The generator matrix

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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+2508x^140+7278x^144+10944x^148+14388x^152+15564x^156+11061x^160+3432x^164+348x^168+12x^176

The gray image is a linear code over GF(4) with n=204, k=8 and d=140.
This code was found by Heurico 1.16 in 35.6 seconds.