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

generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+252x^86+240x^87+30x^88+144x^90+18x^92+108x^94+144x^95+9x^96+72x^98+6x^100

The gray image is a linear code over GF(4) with n=120, k=5 and d=86.
This code was found by Heurico 1.16 in 2.14 seconds.