The generator matrix

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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+126x^140+309x^144+429x^148+885x^152+1983x^156+4128x^160+4749x^164+2616x^168+342x^172+330x^176+255x^180+120x^184+81x^188+24x^192+3x^196+3x^200

The gray image is a linear code over GF(4) with n=216, k=7 and d=140.
This code was found by Heurico 1.16 in 2.33 seconds.