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 a*X  1  1  1  1 a*X
 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*X+a a^2*X+a^2 a^2*X+1 a^2 a*X+a a^2*X a*X+1  1  X  a a^2*X+a^2 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  X a^2 X+a X+a a^2*X+a^2 a^2*X  0 a*X+1 X+1  1  1 X+a
 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 a^2*X a*X  X a^2*X a*X a*X a*X  0 a^2*X  X  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+1236x^199+477x^200+2136x^203+972x^204+2436x^207+795x^208+2388x^211+771x^212+1872x^215+402x^216+1380x^219+342x^220+648x^223+258x^224+192x^227+75x^228+3x^232

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 10 seconds.