The generator matrix

 1  0  1  1  1  1  1  1  1  1  0  1  1  1  X  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  a a^2*X+a^2  0 a^2*X+1 a^2*X+a^2  X  a  1 a^2*X+1 X+a a*X+a^2  1  X  1 X+a a*X+a^2  1  0  X a^2*X+1 a*X+1 a*X+1 a*X  a X+a a*X+a a*X a*X
 0  0 a^2*X a*X  X  X  0 a^2*X a*X a^2*X a^2*X  X  0 a*X a*X a^2*X a*X  X  0  X a*X  X a*X a^2*X  X  0  0 a^2*X  X a^2*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+93x^88+144x^89+96x^90+207x^92+96x^93+72x^94+78x^96+144x^97+63x^100+24x^102+6x^108

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 3.24e-008 seconds.