The generator matrix

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

generates a code of length 28 over F4[X]/(X^2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+852x^75+387x^76+2472x^79+1044x^80+3312x^83+1257x^84+4056x^87+1044x^88+1596x^91+315x^92+39x^96+3x^100+6x^108

The gray image is a linear code over GF(4) with n=112, k=7 and d=75.
This code was found by Heurico 1.16 in 4.1 seconds.