The generator matrix

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

generates a code of length 31 over F4[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+204x^77+456x^78+744x^79+993x^80+1428x^81+3084x^82+3096x^83+3924x^84+5148x^85+7980x^86+7848x^87+10659x^88+13944x^89+16488x^90+14160x^91+20583x^92+22452x^93+25104x^94+16920x^95+21459x^96+19476x^97+16140x^98+10584x^99+7479x^100+4932x^101+4476x^102+1944x^103+330x^104+69x^108+27x^112+9x^116+3x^120

The gray image is a linear code over GF(4) with n=124, k=9 and d=77.
This code was found by Heurico 1.16 in 137 seconds.