The generator matrix

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

generates a code of length 32 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+300x^86+324x^87+507x^88+264x^89+1188x^90+972x^91+939x^92+384x^93+1548x^94+1188x^95+1188x^96+432x^97+1644x^98+1476x^99+1005x^100+384x^101+1176x^102+648x^103+417x^104+72x^105+288x^106+21x^108+15x^112+3x^116

The gray image is a linear code over GF(4) with n=128, k=7 and d=86.
This code was found by Heurico 1.16 in 0.543 seconds.