The generator matrix

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

generates a code of length 32 over F4[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+468x^86+396x^87+144x^88+1668x^90+1368x^91+300x^92+2220x^94+1584x^95+195x^96+2844x^98+1896x^99+204x^100+1680x^102+900x^103+150x^104+336x^106+24x^108+6x^120

The gray image is a linear code over GF(4) with n=128, k=7 and d=86.
This code was found by Heurico 1.16 in 0.93 seconds.