The generator matrix

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

generates a code of length 29 over F4[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+717x^80+966x^84+1269x^88+936x^92+180x^96+18x^100+3x^104+6x^112

The gray image is a linear code over GF(4) with n=116, k=6 and d=80.
This code was found by Heurico 1.16 in 0.281 seconds.