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

generates a code of length 48 over F4[X]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+216x^124+321x^128+483x^132+1005x^136+3033x^140+5673x^144+4344x^148+414x^152+360x^156+228x^160+165x^164+93x^168+39x^172+9x^176

The gray image is a linear code over GF(4) with n=192, k=7 and d=124.
This code was found by Heurico 1.16 in 2.06 seconds.