The generator matrix

 1  0  0  0  1  1  1  X  1  1 aX  X  1  1  1  1  1  1  1  1  1  1  1  X  1  1 (a+1)X  1 aX (a+1)X  1
 0  1  0  0  1  X  1  1 X+1 (a+1)X  1  0  a  a aX+a a+1 a+1 X+a+1 X+1 (a+1)X+a+1 aX+a aX X+1  1 (a+1)X+a  1  1  a aX  1  0
 0  0  1  0 a+1 (a+1)X+1  1 (a+1)X+1 (a+1)X  a (a+1)X+a  1 aX+1  0  a  1 a+1 (a+1)X+a  X X+a X+1 X+1 (a+1)X+1 aX+a+1 X+a+1 aX+a  X X+a+1  1 aX+1  0
 0  0  0  1  1 a+1  X aX+a+1 aX+a+1 X+1 aX+1 (a+1)X+a (a+1)X+1 aX+a a+1 X+a (a+1)X+a+1  0 aX+a (a+1)X+a+1 a+1 aX X+a aX+a (a+1)X+a+1 X+a (a+1)X aX+a X+a+1 X+1  0
 0  0  0  0 (a+1)X  0  0  0  0 aX  X  X  X (a+1)X (a+1)X aX  X aX aX (a+1)X aX  X (a+1)X  X  0 (a+1)X aX  X (a+1)X (a+1)X  X

generates a code of length 31 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+108x^76+156x^77+228x^78+732x^79+1500x^80+1632x^81+1692x^82+3492x^83+5313x^84+6240x^85+3900x^86+9288x^87+12924x^88+14592x^89+8328x^90+20568x^91+22413x^92+24444x^93+11916x^94+25596x^95+24324x^96+20832x^97+8700x^98+12420x^99+10248x^100+5736x^101+2100x^102+1632x^103+882x^104+96x^105+69x^108+33x^112+9x^116

The gray image is a linear code over GF(4) with n=124, k=9 and d=76.
This code was found by Heurico 1.16 in 94.5 seconds.