The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+124x^73+797x^74+1120x^75+1704x^76+1918x^77+1964x^78+2030x^79+1939x^80+1282x^81+1253x^82+906x^83+635x^84+306x^85+219x^86+100x^87+23x^88+18x^89+16x^90+2x^91+17x^92+5x^94+2x^95+1x^96+2x^98

The gray image is a code over GF(2) with n=632, k=14 and d=292.
This code was found by Heurico 1.16 in 3.75 seconds.