The generator matrix

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

generates a code of length 33 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+129x^84+132x^85+48x^86+672x^87+1158x^88+792x^89+168x^90+1968x^91+3042x^92+1944x^93+528x^94+4080x^95+5616x^96+4464x^97+960x^98+6864x^99+8178x^100+4788x^101+960x^102+5808x^103+5916x^104+2904x^105+408x^106+2112x^107+1407x^108+336x^109+69x^112+51x^116+24x^120+9x^124

The gray image is a linear code over GF(4) with n=132, k=8 and d=84.
This code was found by Heurico 1.16 in 8.53 seconds.