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  0  1  1 a*X a^2*X
 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  1 a^2 a*X+1  1  X
 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 X+1 a*X+1 a^2  a  X  X
 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 X+a a*X+a  X  X a*X+a^2  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+384x^75+759x^76+924x^77+984x^78+1968x^79+2148x^80+1944x^81+1656x^82+4620x^83+3981x^84+3348x^85+3048x^86+7836x^87+5931x^88+4860x^89+3816x^90+6756x^91+4152x^92+2400x^93+1248x^94+1476x^95+909x^96+348x^97+33x^100+3x^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 6.2 seconds.