The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+36x^79+190x^80+40x^81+160x^82+44x^83+160x^84+64x^85+128x^86+44x^87+44x^88+24x^89+32x^90+4x^91+47x^92+1x^96+4x^112+1x^124

The gray image is a code over GF(2) with n=336, k=10 and d=158.
This code was found by Heurico 1.16 in 0.482 seconds.