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

generates a code of length 31 over F4[X]/(X^2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+45x^92+192x^93+15x^96+3x^124

The gray image is a linear code over GF(4) with n=124, k=4 and d=92.
As d=92 is an upper bound for linear (124,4,4)-codes, this code is optimal over F4[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in -6.87e-008 seconds.