The generator matrix

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

generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+180x^74+480x^75+516x^76+900x^77+1824x^78+2760x^79+2736x^80+3396x^81+6384x^82+7392x^83+7113x^84+8796x^85+17040x^86+15600x^87+14229x^88+17496x^89+30948x^90+21504x^91+17946x^92+17772x^93+23280x^94+16008x^95+9474x^96+6468x^97+6360x^98+3840x^99+1125x^100+468x^101+54x^104+36x^108+15x^112+3x^120

The gray image is a linear code over GF(4) with n=120, k=9 and d=74.
This code was found by Heurico 1.16 in 88.3 seconds.