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

generates a code of length 36 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+60x^92+96x^93+84x^94+324x^95+963x^96+852x^97+168x^98+1596x^99+2406x^100+1992x^101+444x^102+3348x^103+4878x^104+3000x^105+720x^106+6408x^107+7890x^108+4704x^109+876x^110+6876x^111+6405x^112+3444x^113+648x^114+2844x^115+2730x^116+1176x^117+132x^118+108x^119+171x^120+96x^121+42x^124+27x^128+24x^132+3x^136

The gray image is a linear code over GF(4) with n=144, k=8 and d=92.
This code was found by Heurico 1.16 in 9.59 seconds.