The generator matrix

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

generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+51x^76+60x^77+120x^79+309x^80+444x^81+480x^83+546x^84+984x^85+1680x^87+1107x^88+1848x^89+2400x^91+1218x^92+2028x^93+1464x^95+633x^96+780x^97+105x^100+63x^104+45x^108+15x^112+3x^116

The gray image is a linear code over GF(4) with n=120, k=7 and d=76.
This code was found by Heurico 1.16 in 0.576 seconds.