The generator matrix

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

generates a code of length 49 over F4[X]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+252x^140+780x^141+285x^144+1068x^145+168x^148+600x^149+108x^152+240x^153+177x^156+300x^157+30x^160+84x^161+3x^172

The gray image is a linear code over GF(4) with n=196, k=6 and d=140.
This code was found by Heurico 1.16 in 0.062 seconds.