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

generates a code of length 49 over F4[X]/(X^2) who´s minimum homogenous weight is 132.

Homogenous weight enumerator: w(x)=1x^0+60x^132+183x^136+183x^140+906x^144+2427x^148+102x^152+51x^156+57x^160+39x^164+36x^168+18x^172+21x^176+6x^180+3x^184+3x^192

The gray image is a linear code over GF(4) with n=196, k=6 and d=132.
This code was found by Heurico 1.16 in 0.147 seconds.