The generator matrix

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

generates a code of length 28 over F4[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+171x^68+228x^69+288x^70+840x^71+1977x^72+1884x^73+2664x^74+3816x^75+6753x^76+5640x^77+7536x^78+10416x^79+15417x^80+13416x^81+17568x^82+22560x^83+24921x^84+18852x^85+23184x^86+22584x^87+21849x^88+13116x^89+9336x^90+7224x^91+6597x^92+2160x^93+864x^94+144x^95+66x^96+48x^100+18x^104+6x^108

The gray image is a linear code over GF(4) with n=112, k=9 and d=68.
This code was found by Heurico 1.16 in 78.5 seconds.