The generator matrix

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

generates a code of length 32 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+303x^84+108x^85+156x^86+834x^88+528x^89+336x^90+1326x^92+1608x^93+936x^94+1965x^96+2448x^97+1104x^98+1896x^100+1452x^101+540x^102+648x^104+90x^108+66x^112+33x^116+6x^120

The gray image is a linear code over GF(4) with n=128, k=7 and d=84.
This code was found by Heurico 1.16 in 8.79 seconds.