The generator matrix

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

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+45x^84+96x^87+324x^88+312x^89+444x^91+567x^92+672x^93+1248x^95+768x^96+1872x^97+2232x^99+1089x^100+2208x^101+1824x^103+837x^104+1080x^105+300x^107+300x^108+78x^112+60x^116+21x^120+3x^124+3x^128

The gray image is a linear code over GF(4) with n=132, k=7 and d=84.
This code was found by Heurico 1.16 in 0.647 seconds.