The generator matrix

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

generates a code of length 32 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+288x^83+324x^84+576x^85+1476x^86+1380x^87+1374x^88+1368x^89+2808x^90+3276x^91+3081x^92+2760x^93+4968x^94+4992x^95+4584x^96+3960x^97+6192x^98+5712x^99+4185x^100+3096x^101+4020x^102+2556x^103+1272x^104+528x^105+504x^106+228x^107+15x^108+9x^112+3x^116

The gray image is a linear code over GF(4) with n=128, k=8 and d=83.
This code was found by Heurico 1.16 in 7.6 seconds.