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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 132.

Homogenous weight enumerator: w(x)=1x^0+141x^132+369x^136+414x^140+48x^141+450x^144+576x^145+393x^148+2592x^149+381x^152+5184x^153+459x^156+3888x^157+447x^160+345x^164+324x^168+216x^172+99x^176+45x^180+6x^184+3x^188+3x^192

The gray image is a linear code over GF(4) with n=204, k=7 and d=132.
This code was found by Heurico 1.16 in 2.18 seconds.