The generator matrix

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

generates a code of length 69 over F4[X]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+1443x^196+3042x^200+3411x^204+3147x^208+2553x^212+1515x^216+897x^220+372x^224+3x^232

The gray image is a linear code over GF(4) with n=276, k=7 and d=196.
This code was found by Heurico 1.16 in 22 seconds.