The generator matrix

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

generates a code of length 32 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+393x^80+240x^81+120x^82+1620x^83+2955x^84+2100x^85+1560x^86+4932x^87+8967x^88+6000x^89+4728x^90+11100x^91+20220x^92+12696x^93+10560x^94+18840x^95+31668x^96+18816x^97+13560x^98+20604x^99+28329x^100+12756x^101+5928x^102+9348x^103+9438x^104+2688x^105+408x^106+1140x^107+360x^108+36x^112+18x^116+9x^120+6x^124

The gray image is a linear code over GF(4) with n=128, k=9 and d=80.
This code was found by Heurico 1.16 in 98.6 seconds.