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

generates a code of length 31 over F4[X,sigma]/(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.