The generator matrix

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

generates a code of length 29 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+156x^76+216x^77+48x^78+516x^79+786x^80+816x^81+180x^82+900x^83+1596x^84+1524x^85+180x^86+924x^87+2055x^88+1764x^89+252x^90+1068x^91+1587x^92+996x^93+108x^94+432x^95+195x^96+60x^97+18x^100+3x^104+3x^108

The gray image is a linear code over GF(4) with n=116, k=7 and d=76.
This code was found by Heurico 1.16 in 0.36 seconds.