The generator matrix

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

generates a code of length 34 over F4[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+909x^96+1476x^100+684x^104+780x^108+246x^112

The gray image is a linear code over GF(4) with n=136, k=6 and d=96.
This code was found by Heurico 1.16 in 0.188 seconds.