The generator matrix

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

generates a code of length 70 over F4[X]/(X^2) who´s minimum homogenous weight is 194.

Homogenous weight enumerator: w(x)=1x^0+312x^194+432x^195+657x^196+960x^197+1428x^198+1440x^199+1695x^200+2040x^201+2772x^202+2148x^203+2193x^204+2448x^205+3540x^206+2712x^207+2748x^208+2964x^209+3816x^210+3156x^211+2901x^212+2916x^213+3600x^214+2784x^215+2511x^216+2256x^217+2820x^218+1788x^219+1563x^220+1320x^221+1380x^222+744x^223+477x^224+420x^225+264x^226+156x^227+102x^228+36x^229+36x^230

The gray image is a linear code over GF(4) with n=280, k=8 and d=194.
This code was found by Heurico 1.16 in 19.8 seconds.