The generator matrix

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

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+213x^76+264x^77+108x^78+504x^79+1350x^80+1644x^81+204x^82+1572x^83+3453x^84+3444x^85+744x^86+3744x^87+6741x^88+6408x^89+840x^90+5400x^91+8787x^92+6720x^93+876x^94+3720x^95+4527x^96+2892x^97+300x^98+420x^99+414x^100+132x^101+57x^104+42x^108+12x^112+3x^116

The gray image is a linear code over GF(4) with n=120, k=8 and d=76.
This code was found by Heurico 1.16 in 7.6 seconds.