The generator matrix

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

generates a code of length 70 over F4[X]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+306x^196+348x^197+168x^198+828x^200+768x^201+408x^202+1152x^204+864x^205+564x^206+1266x^208+1260x^209+624x^210+1392x^212+1452x^213+816x^214+1419x^216+936x^217+408x^218+477x^220+408x^221+84x^222+189x^224+108x^225+45x^228+36x^232+18x^236+6x^240+15x^244+12x^248+3x^252+3x^264

The gray image is a linear code over GF(4) with n=280, k=7 and d=196.
This code was found by Heurico 1.16 in 61.5 seconds.