The generator matrix

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

generates a code of length 34 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+444x^89+324x^90+672x^91+1020x^92+1956x^93+1572x^94+1944x^95+2025x^96+3372x^97+2976x^98+3180x^99+3165x^100+5796x^101+4704x^102+5196x^103+4014x^104+6336x^105+4476x^106+3492x^107+2565x^108+3144x^109+1308x^110+876x^111+498x^112+456x^113+15x^116+6x^120+3x^124

The gray image is a linear code over GF(4) with n=136, k=8 and d=89.
This code was found by Heurico 1.16 in 8.94 seconds.