The generator matrix

 1  0  0  0  1  1  1 a^2*X a*X  1  1  0  1  1  1  1  1  1  1  1 a^2*X  X  1  1 a*X  1  1  1 a^2*X  X  1  1  1  1  1
 0  1  0  0  1  X a^2*X+1  1  1 a^2*X  1 a*X  a a*X+a X+a^2 X+a^2 a^2*X+a^2 a*X+a a^2*X+a X+a  1 a^2*X a*X  1  1  0 X+a a^2  1  1 a^2*X+a^2 X+a^2 X+a a^2*X+1  0
 0  0  1  0 a^2 a^2*X+1  a  a a^2*X+a^2 X+a X+1  1  1 a^2*X+a X+a X+1 a*X+a^2  X a^2*X+a a^2*X+a^2 a^2*X+a  1 a*X+a^2 a*X+a  0 a*X+a^2 a^2*X+1 X+1 a*X a*X+1  X a^2*X a^2*X+a^2 a*X+a^2 a^2*X
 0  0  0  1  1 a^2  a X+1 a*X+a a^2*X+1 a^2*X X+a X+1 X+a^2  X a^2*X+a a^2 a^2*X+a a*X X+1 a^2*X X+a^2  1 a^2*X+1 a^2*X+a a*X+a^2 X+a^2 X+a^2 a^2  a a*X+a^2 a^2*X+1 a^2*X+a^2 a*X+1  X
 0  0  0  0 a^2*X  0 a^2*X a^2*X a^2*X a^2*X  0  X a*X  0  X a^2*X a^2*X  0 a*X  0  X a^2*X  0 a*X a*X a*X a^2*X a*X a*X a^2*X a^2*X  X  0  0 a*X

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

Homogenous weight enumerator: w(x)=1x^0+294x^88+276x^89+192x^90+876x^91+2301x^92+1644x^93+1428x^94+3384x^95+8568x^96+5448x^97+4248x^98+7104x^99+16827x^100+13452x^101+8424x^102+14352x^103+27354x^104+22116x^105+11568x^106+17100x^107+29241x^108+19140x^109+9252x^110+10392x^111+15192x^112+5280x^113+1752x^114+2088x^115+2520x^116+228x^117+51x^120+36x^124+9x^128+3x^132+3x^136

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.