The generator matrix

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

generates a code of length 28 over F4[X]/(X^2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+216x^71+672x^72+276x^73+444x^74+1524x^75+1995x^76+1296x^77+1056x^78+3408x^79+3555x^80+4056x^81+2808x^82+6696x^83+5949x^84+6096x^85+3264x^86+6840x^87+5244x^88+3636x^89+1644x^90+2820x^91+1893x^92+69x^96+51x^100+24x^104+3x^112

The gray image is a linear code over GF(4) with n=112, k=8 and d=71.
This code was found by Heurico 1.16 in 75.3 seconds.