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

generates a code of length 31 over F4[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+141x^88+192x^90+576x^94+87x^96+24x^112+3x^120

The gray image is a linear code over GF(4) with n=124, k=5 and d=88.
This code was found by Heurico 1.16 in 1.98 seconds.