The generator matrix

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

generates a code of length 29 over F4[X]/(X^2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+528x^75+834x^76+744x^77+564x^78+2472x^79+2097x^80+1692x^81+1656x^82+4524x^83+4545x^84+3132x^85+2880x^86+7884x^87+6483x^88+4404x^89+3144x^90+7284x^91+4635x^92+2028x^93+972x^94+1884x^95+834x^96+288x^97+15x^100+9x^104+3x^108

The gray image is a linear code over GF(4) with n=116, k=8 and d=75.
This code was found by Heurico 1.16 in 7.35 seconds.