The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+160x^73+759x^74+1194x^75+1732x^76+1564x^77+2242x^78+1978x^79+1997x^80+1296x^81+1281x^82+720x^83+681x^84+396x^85+205x^86+98x^87+33x^88+8x^89+24x^90+4x^91+3x^92+1x^94+4x^95+1x^96+2x^99

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 3.84 seconds.