The generator matrix

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

generates a code of length 28 over F4[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+642x^72+336x^73+756x^74+828x^75+2505x^76+1344x^77+2160x^78+2352x^79+5199x^80+2304x^81+3456x^82+4392x^83+8868x^84+3840x^85+4536x^86+5040x^87+7740x^88+2544x^89+2700x^90+1212x^91+2145x^92+384x^93+216x^94+18x^96+18x^100

The gray image is a linear code over GF(4) with n=112, k=8 and d=72.
This code was found by Heurico 1.16 in 6.49 seconds.