The generator matrix

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

generates a code of length 34 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+96x^93+240x^94+96x^96+360x^97+552x^98+57x^100+360x^101+648x^102+45x^104+504x^105+696x^106+30x^108+216x^109+168x^110+3x^112+15x^120+6x^124+3x^132

The gray image is a linear code over GF(4) with n=136, k=6 and d=93.
This code was found by Heurico 1.16 in 18.2 seconds.