The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+208x^73+357x^74+420x^75+392x^76+416x^77+332x^78+350x^79+255x^80+272x^81+225x^82+230x^83+176x^84+116x^85+90x^86+76x^87+56x^88+48x^89+24x^90+26x^91+8x^92+12x^93+4x^94+2x^95

The gray image is a code over GF(2) with n=316, k=12 and d=146.
This code was found by Heurico 1.11 in 0.544 seconds.