The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1
 0  X  0  0  0  0  X  X  X a*X  0  X a^2*X a*X a^2*X a*X  X  X a*X  0 a^2*X a*X  X a*X  0  X  0 a^2*X a*X  X a^2*X a*X  0  0 a*X a*X  X a^2*X  X a^2*X a^2*X  0 a^2*X a*X a*X a*X  X  X  0 a*X  0  X  0 a*X a*X  0  X a*X  X a*X  X  0  X  0 a*X  X  0 a^2*X  0  0
 0  0  X  0  0  X a^2*X a*X a*X a*X  0  0 a*X a*X  0 a*X a^2*X a*X a^2*X a^2*X  0  X a^2*X  0 a^2*X  0 a*X a*X a*X a*X a^2*X  0 a^2*X a^2*X  0  0 a^2*X  X  X  0 a*X  0  X a*X  X  X a*X  X  X  0  0 a*X a*X a*X  X a*X  0 a^2*X a^2*X  0 a^2*X a*X a*X a^2*X  0 a*X a^2*X a*X  0 a^2*X
 0  0  0  X  0 a^2*X  0  X a*X a^2*X  X  X  X  0  X a^2*X  X  X a^2*X a^2*X a^2*X a*X  0 a^2*X a^2*X  0  X a*X  0 a^2*X  0 a*X  X  X a*X  0 a*X  0  X a^2*X  0 a^2*X  0 a*X  X a*X a*X  X a*X a^2*X  X  X a^2*X a^2*X  0  X a^2*X  X  0  X  X a^2*X  X a*X  X a^2*X  0  0 a^2*X a^2*X
 0  0  0  0  X  X  X a^2*X  X  X  X a*X  0  0  0 a*X  X a*X a^2*X a^2*X a*X  0 a*X  X a*X a*X  0  0 a^2*X a^2*X a^2*X a*X  X  0  0  X a*X a*X  X  0 a*X  X a^2*X a^2*X  X a^2*X a^2*X a^2*X  X a^2*X a*X  X a^2*X  0 a^2*X a*X a*X a*X a^2*X  X a*X  0  0 a*X a^2*X  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+147x^196+174x^200+192x^204+768x^207+129x^208+2304x^211+69x^212+84x^216+39x^220+48x^224+27x^228+30x^232+39x^236+24x^240+12x^244+6x^248+3x^276

The gray image is a linear code over GF(4) with n=280, k=6 and d=196.
This code was found by Heurico 1.16 in 0.407 seconds.