The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+159x^76+704x^77+974x^78+1330x^79+743x^80+1170x^81+675x^82+878x^83+382x^84+422x^85+316x^86+196x^87+93x^88+72x^89+32x^90+28x^91+13x^92+2x^94+1x^96+1x^98

The gray image is a code over GF(2) with n=648, k=13 and d=304.
This code was found by Heurico 1.16 in 1.16 seconds.