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

generates a code of length 47 over F4[X]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+126x^120+309x^124+417x^128+447x^132+768x^135+468x^136+4608x^139+441x^140+6912x^143+417x^144+423x^148+441x^152+267x^156+189x^160+123x^164+21x^168+3x^172+3x^180

The gray image is a linear code over GF(4) with n=188, k=7 and d=120.
This code was found by Heurico 1.16 in 1.95 seconds.