The generator matrix

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

generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+606x^60+1164x^62+3009x^64+2928x^66+8067x^68+7272x^70+15240x^72+8880x^74+12345x^76+4332x^78+1554x^80+93x^84+36x^88+9x^92

The gray image is a linear code over GF(4) with n=96, k=8 and d=60.
This code was found by Heurico 1.16 in 53.2 seconds.