The generator matrix

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

generates a code of length 35 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+231x^88+420x^89+192x^90+768x^91+1815x^92+2772x^93+1656x^94+3396x^95+5487x^96+7632x^97+4440x^98+8196x^99+12936x^100+16392x^101+8160x^102+15864x^103+22329x^104+26580x^105+11232x^106+20184x^107+22527x^108+23508x^109+8808x^110+11268x^111+10467x^112+7992x^113+2376x^114+1764x^115+1935x^116+720x^117+24x^120+42x^124+21x^128+9x^132

The gray image is a linear code over GF(4) with n=140, k=9 and d=88.
This code was found by Heurico 1.16 in 111 seconds.