The generator matrix

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

generates a code of length 31 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+288x^86+390x^88+1368x^90+192x^92+456x^94+231x^96+744x^98+192x^100+216x^102+18x^104

The gray image is a linear code over GF(4) with n=124, k=6 and d=86.
This code was found by Heurico 1.16 in 0.031 seconds.