The generator matrix

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

generates a code of length 29 over F4[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+51x^72+24x^73+252x^74+336x^75+279x^76+1404x^77+1032x^78+1608x^79+561x^80+3648x^81+2100x^82+3552x^83+909x^84+9192x^85+3216x^86+6288x^87+918x^88+11016x^89+3588x^90+5520x^91+891x^92+5436x^93+1896x^94+1128x^95+339x^96+204x^98+111x^100+15x^104+18x^108+3x^112

The gray image is a linear code over GF(4) with n=116, k=8 and d=72.
This code was found by Heurico 1.16 in 6.89 seconds.