The generator matrix

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

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+75x^88+96x^90+72x^92+9x^96+3x^104

The gray image is a linear code over GF(4) with n=120, k=4 and d=88.
This code was found by Heurico 1.16 in 3.24e-008 seconds.