The generator matrix

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

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+252x^86+240x^87+27x^88+144x^90+27x^92+108x^94+144x^95+72x^98+9x^100

The gray image is a linear code over GF(4) with n=120, k=5 and d=86.
This code was found by Heurico 1.16 in 0.14 seconds.