The generator matrix

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

generates a code of length 70 over F4[X]/(X^2) who´s minimum homogenous weight is 203.

Homogenous weight enumerator: w(x)=1x^0+708x^203+396x^204+984x^207+207x^208+540x^211+150x^212+360x^215+120x^216+252x^219+72x^220+144x^223+48x^224+84x^227+27x^228+3x^244

The gray image is a linear code over GF(4) with n=280, k=6 and d=203.
This code was found by Heurico 1.16 in 0.219 seconds.