The generator matrix

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

generates a code of length 28 over F4[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+378x^76+906x^80+1470x^84+1056x^88+246x^92+21x^96+18x^100

The gray image is a linear code over GF(4) with n=112, k=6 and d=76.
This code was found by Heurico 1.16 in 0.0379 seconds.