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.