The generator matrix

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

generates a code of length 28 over F4[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+69x^64+369x^68+132x^70+972x^72+780x^74+2859x^76+3240x^78+7764x^80+7320x^82+14484x^84+8724x^86+11568x^88+4380x^90+2268x^92+366x^96+171x^100+60x^104+9x^108

The gray image is a linear code over GF(4) with n=112, k=8 and d=64.
This code was found by Heurico 1.16 in 7.24 seconds.