The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+98x^74+176x^75+169x^76+148x^77+103x^78+56x^79+32x^80+56x^81+27x^82+40x^83+52x^84+36x^85+18x^86+8x^90+1x^92+1x^98+1x^102+1x^104

The gray image is a code over GF(2) with n=312, k=10 and d=148.
This code was found by Heurico 1.11 in 0.282 seconds.