The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  0  1  1  1  X  1  X a^2*X  1  0  1
 0  1  1  a a^2  0 a^2*X+1  a a^2*X+a^2  1  0  a a^2*X+1  1 a^2*X+a^2 a^2*X+a^2  a  0  1 a^2*X+a^2  X a*X  1 a^2*X+1  1  1 X+a  1  0
 0  0 a^2*X  0  0  0  X  X  X  X  X a*X a^2*X  X  0  X a^2*X  X  X  0 a^2*X  0 a*X  0  X  X a^2*X a*X  0
 0  0  0  X  0  X a^2*X a*X  0  X a*X  X  X  0  0  0 a^2*X a^2*X a*X a^2*X a*X  X  0 a*X  X a^2*X a^2*X  0  X
 0  0  0  0 a^2*X a^2*X  X  0 a^2*X  X  X  X  X a^2*X a*X  0  X a^2*X  X  0  0 a*X a^2*X a^2*X a*X a*X  0  0 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+42x^72+108x^74+108x^75+225x^76+204x^78+372x^79+762x^80+504x^82+1368x^83+1782x^84+792x^86+2184x^87+2499x^88+924x^90+1788x^91+1581x^92+540x^94+324x^95+123x^96+84x^100+45x^104+24x^108

The gray image is a linear code over GF(4) with n=116, k=7 and d=72.
This code was found by Heurico 1.16 in 0.532 seconds.