The generator matrix

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

generates a code of length 32 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+324x^82+216x^83+459x^84+492x^85+1428x^86+972x^87+927x^88+1224x^89+4308x^90+1896x^91+2088x^92+2952x^93+8040x^94+3528x^95+2913x^96+4224x^97+10380x^98+3864x^99+2685x^100+2988x^101+5604x^102+1740x^103+1011x^104+408x^105+636x^106+72x^107+54x^108+48x^112+42x^116+12x^120

The gray image is a linear code over GF(4) with n=128, k=8 and d=82.
This code was found by Heurico 1.16 in 69.6 seconds.