The generator matrix

 1  0  0  0  1  1  1  1  1  X  1  1  1  1  1  1 a^2*X  X  1  1  1 a*X  0  0 a*X  1  1  1 a*X  1  1  1
 0  1  0  0  0  X  X a^2*X+1 a*X+1  1 a^2*X+a a*X+a a^2 a^2  X a^2*X+1  1  1  1 X+a^2 X+a^2  1  1 a*X  1 a*X+1 X+a^2 a*X+a a^2*X a^2*X X+a a*X
 0  0  1  0  1 a^2*X+a a^2*X+a^2  a a^2*X  a a*X+1  a a^2 a*X+a X+a a^2*X+1 X+1  0 a^2*X+a^2 a^2*X+1 X+a^2 X+a X+a^2  1 a*X+a^2  X a*X a^2*X+1  1 a^2*X a*X a*X+1
 0  0  0  1 a^2  a  1 a*X X+a  a  X a*X+a^2  0 a*X+1 a*X  1 a*X+a a*X+a^2 a*X+a^2 X+a^2 X+a  1 a*X a*X+a^2 a^2*X+a^2 a*X a^2*X+1 X+a X+a a^2*X+1 a^2*X+a^2 a^2*X+a
 0  0  0  0  X  0 a*X  0  0  0  X  X  X a^2*X a^2*X a^2*X  X  X a*X a*X a^2*X  X a*X  X  0  X a*X  0 a^2*X  0 a^2*X  X

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

Homogenous weight enumerator: w(x)=1x^0+240x^80+480x^81+432x^82+1128x^83+2235x^84+3312x^85+1860x^86+4500x^87+7260x^88+8652x^89+4116x^90+10884x^91+16374x^92+17760x^93+7800x^94+20760x^95+27375x^96+27288x^97+9768x^98+20928x^99+22755x^100+17808x^101+5508x^102+8916x^103+7509x^104+4572x^105+1236x^106+468x^107+126x^108+54x^112+24x^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 95.3 seconds.