The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  X a^2*X a^2*X  0  1  1 a*X  1  1
 0  1  0 a^2*X a*X  X  1 a^2*X+1  a X+1 a^2*X+a^2 a^2*X+a a*X+a X+a^2 a*X+a^2 a*X+1 X+a a^2  1  1  1  1  1  1  X  0  1  1 a^2*X+1
 0  0  1  1  a a^2 X+a^2 X+a  X a*X a*X+a^2 X+1 a^2*X+a a^2*X+1 a^2*X a*X+1 a^2*X+a^2 a*X+a X+1 a^2*X a*X  1 X+1 X+a a^2*X+1 a*X+a^2  0 X+a  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+213x^80+204x^81+240x^82+144x^83+720x^84+468x^85+264x^86+96x^87+312x^88+180x^89+96x^90+144x^91+378x^92+300x^93+168x^94+162x^96+6x^100

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 0.016 seconds.