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

generates a code of length 49 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+60x^124+246x^128+396x^132+48x^135+414x^136+576x^139+447x^140+2592x^143+429x^144+5184x^147+396x^148+3888x^151+426x^152+435x^156+357x^160+207x^164+180x^168+66x^172+27x^176+9x^180

The gray image is a linear code over GF(4) with n=196, k=7 and d=124.
This code was found by Heurico 1.16 in 2.05 seconds.