The generator matrix

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

generates a code of length 49 over F4[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+372x^138+249x^140+648x^142+240x^144+792x^146+186x^148+576x^150+231x^152+468x^154+93x^156+216x^158+15x^160+3x^168+6x^176

The gray image is a linear code over GF(4) with n=196, k=6 and d=138.
This code was found by Heurico 1.16 in 0.0937 seconds.