The generator matrix

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

generates a code of length 40 over F4[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+912x^110+585x^112+2124x^114+984x^116+3168x^118+1047x^120+2904x^122+936x^124+2352x^126+420x^128+828x^130+96x^132+21x^136+6x^144

The gray image is a linear code over GF(4) with n=160, k=7 and d=110.
This code was found by Heurico 1.16 in 87.5 seconds.