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+1)X aX  X  X aX aX (a+1)X aX  0 (a+1)X (a+1)X  X aX aX (a+1)X (a+1)X  X aX  X (a+1)X  0 (a+1)X  0  X (a+1)X (a+1)X  0 aX  X  X (a+1)X aX  0  0
 0  0  X  0  0  0  0  X  X  X aX (a+1)X (a+1)X aX  0 (a+1)X aX  X aX (a+1)X (a+1)X (a+1)X  0 (a+1)X aX  0  X  0  X  X  0  X  X  X  X aX aX (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X  X  X  X  0  0
 0  0  0  X  0  0  X (a+1)X (a+1)X aX  0  0  X  0  X (a+1)X aX  X (a+1)X (a+1)X  X  X  X aX  X  0 (a+1)X aX (a+1)X aX  X (a+1)X  0 (a+1)X (a+1)X  0  X  0 (a+1)X  X  0  X (a+1)X  X  X (a+1)X aX
 0  0  0  0  X  0 (a+1)X  0 (a+1)X  X aX  X  0  X aX (a+1)X aX aX aX aX  0 aX aX aX (a+1)X aX  0 aX  0 (a+1)X  0  X  0  0  X  X aX  X  0 aX aX aX (a+1)X aX  X (a+1)X (a+1)X
 0  0  0  0  0  X  X  X (a+1)X (a+1)X (a+1)X (a+1)X  0  X (a+1)X  X  X  0 aX  X  X (a+1)X  0  X  0 aX (a+1)X aX (a+1)X (a+1)X (a+1)X aX aX  0  X  X  X  0  X  X  0 aX  0 aX (a+1)X  0 aX

generates a code of length 47 over F4[X,sigma]/(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 1.97 seconds.