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

generates a code of length 71 over F4[X]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+42x^196+72x^197+120x^199+513x^200+156x^201+384x^203+1170x^204+444x^205+540x^207+1767x^208+516x^209+456x^211+1908x^212+600x^213+576x^215+2499x^216+612x^217+480x^219+1656x^220+492x^221+396x^223+483x^224+156x^225+120x^227+66x^228+24x^229+45x^232+30x^236+21x^240+24x^244+9x^248+6x^264

The gray image is a linear code over GF(4) with n=284, k=7 and d=196.
This code was found by Heurico 1.16 in 1.6 seconds.