The generator matrix

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

generates a code of length 49 over F4[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+480x^136+300x^137+564x^139+1767x^140+696x^141+684x^143+2484x^144+552x^145+624x^147+2253x^148+696x^149+720x^151+1890x^152+468x^153+348x^155+1077x^156+240x^157+132x^159+270x^160+120x^161+15x^164+3x^176

The gray image is a linear code over GF(4) with n=196, k=7 and d=136.
This code was found by Heurico 1.16 in 0.672 seconds.