The generator matrix

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

generates a code of length 70 over F4[X]/(X^2) who´s minimum homogenous weight is 199.

Homogenous weight enumerator: w(x)=1x^0+1164x^199+498x^200+2304x^203+930x^204+2400x^207+774x^208+2388x^211+702x^212+1728x^215+600x^216+1356x^219+324x^220+804x^223+204x^224+144x^227+57x^228+3x^240+3x^244

The gray image is a linear code over GF(4) with n=280, k=7 and d=199.
This code was found by Heurico 1.16 in 27.9 seconds.