The generator matrix

 1  0  0  0  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1 a*X  1  1  1  1  1 a*X  1  1  1
 0  1  0  0  0  X  X a^2*X+1 a*X+1  1 a^2*X+a a*X+a a^2*X+1 a^2*X+a a^2*X+1 a*X+a a*X+a^2 a^2*X a*X+a^2  1 a^2*X+a^2  1 a*X a*X a*X+a  1 a^2*X+a^2 a^2*X a^2*X+a^2
 0  0  1  0  1 a^2*X+a a^2*X+a^2  a a^2*X  a a*X+1  a a^2 a^2*X+a^2 X+a^2 X+1 X+1 a^2*X+a^2 X+1  1  a  1 X+a  0 a*X+a a^2*X+a^2 X+a^2 a^2*X+a X+a^2
 0  0  0  1 a^2  a  1 a*X X+a  a  X a*X+a^2 a*X+a^2 a^2*X+a  0 a^2 a^2*X a^2*X+a a^2*X+1 a^2*X X+1 a^2*X+1 a^2*X+a^2 a*X+a  1 a^2*X+a^2 a*X+a^2 a*X a^2*X
 0  0  0  0  X  0 a*X  0  0  0  X  X a^2*X a^2*X a*X a^2*X a*X  X  X a^2*X a^2*X a*X a^2*X a*X  X  X a*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+507x^72+576x^73+744x^74+1140x^75+3105x^76+3516x^77+3420x^78+3576x^79+8220x^80+10536x^81+10404x^82+7704x^83+18366x^84+22344x^85+19032x^86+15840x^87+25260x^88+27552x^89+20976x^90+11220x^91+18234x^92+14364x^93+6732x^94+3528x^95+4002x^96+984x^97+132x^98+69x^100+39x^104+15x^108+3x^112+3x^116

The gray image is a linear code over GF(4) with n=116, k=9 and d=72.
This code was found by Heurico 1.16 in 84.5 seconds.