The generator matrix

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

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+234x^72+96x^73+156x^74+645x^76+576x^77+336x^78+1353x^80+1536x^81+936x^82+2385x^84+2496x^85+1104x^86+2001x^88+1440x^89+540x^90+381x^92+102x^96+39x^100+21x^104+6x^108

The gray image is a linear code over GF(4) with n=112, k=7 and d=72.
This code was found by Heurico 1.16 in 0.572 seconds.