The generator matrix

 1  0  0  1  1  1  2  2 2X+2  1  1  2  1  1 3X  1  1 X+2 3X+2  1  1  1  X  1  1  1  0 2X 3X+2  1  2  1  1  1 X+2  1  1 2X  1  1  1 3X+2 3X 3X  1  0 X+2  1  1  0  1 3X 3X X+2  1 2X  1  1  1  1  1  1  1  1  1  2 X+2  1  1  1  1 X+2  1  1  1  1  1  1  1  1
 0  1  0  0 2X+3 2X+3  1 3X  1 2X  3  1  2 2X+1 3X+2  X 3X+1  1  1 3X X+1 3X+2  1 X+2 X+3 X+3 2X+2  1  0 X+1  1 2X+2 2X  X  1 3X+1  3  1 3X+3 3X 2X+1  1  1  1  1 3X 2X 2X+1 2X+2  1 X+1 3X  1 X+2  1  0 2X+1 3X+3  0 3X  X 3X+2  3  1 3X+1  1  1 X+2 2X+2 X+3 3X+1 2X+2 2X+3  2 2X 2X  1 3X X+3  0
 0  0  1 X+1 3X+1 2X X+3  1  X 3X  X  3 2X+3  3  1 2X+1 3X X+3 X+2  2  3 X+2  0 3X+3 X+3 2X  1  1  1 2X 3X+1 2X+1 2X+2 2X+3 2X+1 3X+1 2X+2  X 2X+1 X+1  3 3X+1 X+2 2X+2  0  1  1 X+3  2  0 3X+2  1  3  1 X+1  1  1 X+3 X+2  0 X+2 3X  X  X X+3 X+3 3X 2X+1 2X+1  X 3X+2  1 3X+2 3X+3 X+1 2X+3  2 2X X+1  0
 0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X  0  0  0 2X 2X  0 2X  0  0 2X 2X 2X  0  0  0 2X  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X  0  0 2X 2X 2X  0  0

generates a code of length 80 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+168x^75+713x^76+966x^77+1157x^78+1018x^79+1117x^80+744x^81+729x^82+422x^83+351x^84+284x^85+234x^86+128x^87+88x^88+38x^89+23x^90+8x^91+2x^92+1x^102

The gray image is a code over GF(2) with n=640, k=13 and d=300.
This code was found by Heurico 1.16 in 1.16 seconds.